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166 relations: Absolute continuity, Absolute value, Accademia dei Lincei, Aizik Volpert, Almost everywhere, Arc length, Associative algebra, Ball (mathematics), Banach algebra, Banach space, Bibliography, Bibliothèque nationale de France, Boundary (topology), Bounded function, Caccioppoli set, Calculus of variations, Camille Jordan, Cardinality of the continuum, Cartesian coordinate system, Cauchy boundary condition, Cauchy problem, Cauchy sequence, Chain rule, Classification of discontinuities, Codomain, Communications on Pure and Applied Mathematics, Compact space, Complete metric space, Complex measure, Complex number, Comptes rendus de l'Académie des Sciences, Continuous function, Countable set, Dense set, Derivative, Differentiable function, Dimension, Direct method in the calculus of variations, Directional derivative, Disjoint sets, Distance, Distribution (mathematics), Domain of a function, Engineering, Ennio de Giorgi, Ergebnisse der Mathematik und ihrer Grenzgebiete, Essential supremum and essential infimum, Existence theorem, Finite measure, Finite set, ..., First-order partial differential equation, Formula, Fourier series, Function (mathematics), Function composition, Function space, Functional (mathematics), Geometric measure theory, Gianni Dal Maso, Gradient, Graph of a function, Hahn–Banach theorem, Hausdorff measure, Helly's selection theorem, Hyperbolic partial differential equation, Hyperplane, Identity function, Index set, Indexed family, Indicator function, Infimum and supremum, Infinity, Integral, Intersection (set theory), Interval (mathematics), Lamberto Cesari, Laurence Chisholm Young, Lebesgue integration, Lebesgue measure, Lebesgue–Stieltjes integration, Leonida Tonelli, Limit of a function, Limit of a sequence, Limit superior and limit inferior, Linear continuum, Linear form, Linear subspace, Linearity, Lipschitz continuity, List of continuity-related mathematical topics, Local property, Locally integrable function, Lp space, Luigi Ambrosio, Matematicheskii Sbornik, Mathematical analysis, Mathematical model, Mathematical physics, Mathematical proof, Mathematics, Maxima and minima, Measurable function, Measure (mathematics), Minimal surface, Monotonic function, Mumford–Shah functional, Nonlinear system, Norm (mathematics), Normed vector space, Null set, Olga Oleinik, One-sided limit, Open set, Ordinary differential equation, Partial derivative, Partial differential equation, Partition of an interval, Physics, Plane (geometry), Point (geometry), Pointwise product, Probability measure, Proceedings of the American Mathematical Society, Product rule, Radon measure, Real line, Real number, Reduced derivative, Relative direction, Relatively compact subspace, Renato Caccioppoli, Riemann–Stieltjes integral, Riesz representation theorem, Riesz–Markov–Kakutani representation theorem, Russian Mathematical Surveys, Scuola Normale Superiore di Pisa, Semi-continuity, Separable space, Sequence, Set (mathematics), Sigma-algebra, Signed measure, Smoothness, Sobolev space, Space (mathematics), Spectral theory, Spectral theory of ordinary differential equations, Studia Mathematica, Subset, Summation, Support (mathematics), Tony F. Chan, Topological vector space, Topology, Total variation, Transactions of the American Mathematical Society, Uniform norm, Unit vector, Variable (mathematics), Vector space, Vector-valued function, Władysław Orlicz, Weak derivative, Weak solution, Weight function, Young measure. Expand index (116 more) »
Absolute continuity
In calculus, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity.
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Absolute value
In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.
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Accademia dei Lincei
The Accademia dei Lincei (literally the "Academy of the Lynx-Eyed", but anglicised as the Lincean Academy) is an Italian science academy, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy.
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Aizik Volpert
Aizik Isaakovich Vol'pert (Айзик Исаакович Вольперт) (5 June 1923 – January 2006) (the family name is also transliterated as Volpert or WolpertSee.) was a Soviet and Israeli mathematician and chemical engineer working in partial differential equations, functions of bounded variation and chemical kinetics.
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Almost everywhere
In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities.
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Arc length
Determining the length of an irregular arc segment is also called rectification of a curve.
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Associative algebra
In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.
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Ball (mathematics)
In mathematics, a ball is the space bounded by a sphere.
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Banach algebra
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, i.e. a normed space and complete in the metric induced by the norm.
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Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
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Bibliography
Bibliography (from Greek βιβλίον biblion, "book" and -γραφία -graphia, "writing"), as a discipline, is traditionally the academic study of books as physical, cultural objects; in this sense, it is also known as bibliology (from Greek -λογία, -logia).
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Bibliothèque nationale de France
The (BnF, English: National Library of France) is the national library of France, located in Paris.
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Boundary (topology)
In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.
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Bounded function
In mathematics, a function f defined on some set X with real or complex values is called bounded, if the set of its values is bounded.
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Caccioppoli set
In mathematics, a Caccioppoli set is a set whose boundary is measurable and has a (at least locally) finite measure.
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Calculus of variations
Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
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Camille Jordan
Marie Ennemond Camille Jordan (5 January 1838 – 22 January 1922) was a French mathematician, known both for his foundational work in group theory and for his influential Cours d'analyse.
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Cardinality of the continuum
In set theory, the cardinality of the continuum is the cardinality or “size” of the set of real numbers \mathbb R, sometimes called the continuum.
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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Cauchy boundary condition
In mathematics, a Cauchy boundary conditions augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so to ensure that a unique solution exists.
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Cauchy problem
A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain.
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Cauchy sequence
In mathematics, a Cauchy sequence, named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses.
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Chain rule
In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions.
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Classification of discontinuities
Continuous functions are of utmost importance in mathematics, functions and applications.
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Codomain
In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall.
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Communications on Pure and Applied Mathematics
Communications on Pure and Applied Mathematics is a monthly peer-reviewed scientific journal which is published by John Wiley & Sons on behalf of the Courant Institute of Mathematical Sciences.
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Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
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Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary).
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Complex measure
In mathematics, specifically measure theory, a complex measure generalizes the concept of measure by letting it have complex values.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Comptes rendus de l'Académie des Sciences
Comptes rendus de l'Académie des Sciences (English: Proceedings of the Academy of sciences), or simply Comptes rendus, is a French scientific journal which has been published since 1666.
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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Dense set
In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of A, that is the closure of A is constituting the whole set X. Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A — for instance, every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Differentiable function
In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
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Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
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Direct method in the calculus of variations
In the calculus of variations, a topic in mathematics, the direct method is a general method for constructing a proof of the existence of a minimizer for a given functional, introduced by Zaremba and David Hilbert around 1900.
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Directional derivative
In mathematics, the directional derivative of a multivariate differentiable function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v. It therefore generalizes the notion of a partial derivative, in which the rate of change is taken along one of the curvilinear coordinate curves, all other coordinates being constant.
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Disjoint sets
In mathematics, two sets are said to be disjoint sets if they have no element in common.
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Distance
Distance is a numerical measurement of how far apart objects are.
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Distribution (mathematics)
Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.
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Domain of a function
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
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Engineering
Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.
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Ennio de Giorgi
Ennio De Giorgi (8 February 1928 – 25 October 1996) was an Italian mathematician, member of the House of Giorgi, who worked on partial differential equations and the foundations of mathematics.
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Ergebnisse der Mathematik und ihrer Grenzgebiete
Ergebnisse der Mathematik und ihrer Grenzgebiete/A Series of Modern Surveys in Mathematics is a series of scholarly monographs published by Springer Science+Business Media.
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Essential supremum and essential infimum
In mathematics, the concepts of essential supremum and essential infimum are related to the notions of supremum and infimum, but adapted to measure theory and functional analysis, where one often deals with statements that are not valid for all elements in a set, but rather almost everywhere, i.e., except on a set of measure zero.
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Existence theorem
In mathematics, an existence theorem is a theorem with a statement beginning 'there exist(s)..', or more generally 'for all,,...
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Finite measure
In measure theory, a branch of mathematics, a finite measure or totally finite measure is a special measure that always takes on finite values.
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Finite set
In mathematics, a finite set is a set that has a finite number of elements.
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First-order partial differential equation
In mathematics, a first-order partial differential equation is a partial differential equation that involves only first derivatives of the unknown function of n variables.
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Formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula.
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Fourier series
In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
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Function space
In mathematics, a function space is a set of functions between two fixed sets.
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Functional (mathematics)
In mathematics, the term functional (as a noun) has at least two meanings.
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Geometric measure theory
In mathematics, geometric measure theory (GMT) is the study of geometric properties of sets (typically in Euclidean space) through measure theory.
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Gianni Dal Maso
Gianni Dal Maso (born 1954) is an Italian mathematician who is active in the fields of partial differential equations, calculus of variations and applied mathematics.
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Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
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Graph of a function
In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.
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Hahn–Banach theorem
In mathematics, the Hahn–Banach theorem is a central tool in functional analysis.
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Hausdorff measure
In mathematics a Hausdorff measure is a type of outer measure, named for Felix Hausdorff, that assigns a number in to each set in Rn or, more generally, in any metric space.
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Helly's selection theorem
In mathematics, Helly's selection theorem states that a sequence of functions that is locally of bounded total variation and uniformly bounded at a point has a convergent subsequence.
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Hyperbolic partial differential equation
In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first derivatives.
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Hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
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Identity function
Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.
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Index set
In mathematics, an index set is a set whose members label (or index) members of another set.
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Indexed family
In mathematics, an indexed family is informally a collection of objects, each associated with an index from some index set.
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Indicator function
In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. It is usually denoted by a symbol 1 or I, sometimes in boldface or blackboard boldface, with a subscript specifying the subset.
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Infimum and supremum
In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.
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Infinity
Infinity (symbol) is a concept describing something without any bound or larger than any natural number.
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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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Intersection (set theory)
In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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Lamberto Cesari
Lamberto Cesari (23 September 1910 – 12 March 1990) was an Italian mathematician naturalized in the United States, known for his work on the theory of surface area, the theory of functions of bounded variation, the theory of optimal control and on the stability theory of dynamical systems: in particular, by extending the concept of Tonelli plane variation, he succeeded in introducing the class of functions of bounded variation of several variables in its full generality.
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Laurence Chisholm Young
Laurence Chisholm Young (14 July 1905 – 24 December 2000) was an American mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory.
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Lebesgue integration
In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the -axis.
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Lebesgue measure
In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space.
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Lebesgue–Stieltjes integration
In measure-theoretic analysis and related branches of mathematics, Lebesgue–Stieltjes integration generalizes Riemann–Stieltjes and Lebesgue integration, preserving the many advantages of the former in a more general measure-theoretic framework.
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Leonida Tonelli
Leonida Tonelli (19 April 1885 – 12 March 1946) was an Italian mathematician, noted for creating Tonelli's theorem, a variation of Fubini's theorem, and for introducing semicontinuity methods as a common tool for the direct method in the calculus of variations.
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Limit of a function
Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.
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Limit of a sequence
As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.
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Limit superior and limit inferior
In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting (i.e., eventual and extreme) bounds on the sequence.
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Linear continuum
In the mathematical field of order theory, a continuum or linear continuum is a generalization of the real line.
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Linear form
In linear algebra, a linear functional or linear form (also called a one-form or covector) is a linear map from a vector space to its field of scalars.
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Linear subspace
In linear algebra and related fields of mathematics, a linear subspace, also known as a vector subspace, or, in the older literature, a linear manifold, is a vector space that is a subset of some other (higher-dimension) vector space.
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Linearity
Linearity is the property of a mathematical relationship or function which means that it can be graphically represented as a straight line.
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Lipschitz continuity
In mathematical analysis, Lipschitz continuity, named after Rudolf Lipschitz, is a strong form of uniform continuity for functions.
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List of continuity-related mathematical topics
In mathematics, the terms continuity, continuous, and continuum are used in a variety of related ways.
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Local property
In mathematics, a phenomenon is sometimes said to occur locally if, roughly speaking, it occurs on sufficiently small or arbitrarily small neighborhoods of points.
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Locally integrable function
In mathematics, a locally integrable function (sometimes also called locally summable function) is a function which is integrable (so its integral is finite) on every compact subset of its domain of definition.
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Lp space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.
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Luigi Ambrosio
Luigi Ambrosio (born 27 January 1963) is a professor at Scuola Normale Superiore in Pisa, Italy.
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Matematicheskii Sbornik
Matematicheskii Sbornik (Математический сборник, abbreviated Mat. Sb.) is a peer reviewed Russian mathematical journal founded by the Moscow Mathematical Society in 1866.
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Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
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Mathematical model
A mathematical model is a description of a system using mathematical concepts and language.
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Mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics.
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Mathematical proof
In mathematics, a proof is an inferential argument for a mathematical statement.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Maxima and minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
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Measurable function
In mathematics and in particular measure theory, a measurable function is a function between two measurable spaces such that the preimage of any measurable set is measurable, analogously to the definition that a function between topological spaces is continuous if the preimage of each open set is open.
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Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.
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Minimal surface
In mathematics, a minimal surface is a surface that locally minimizes its area.
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Monotonic function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.
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Mumford–Shah functional
The Mumford–Shah functional is a functional that is used to establish an optimality criterion for segmenting an image into sub-regions.
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Nonlinear system
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.
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Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
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Normed vector space
In mathematics, a normed vector space is a vector space over the real or complex numbers, on which a norm is defined.
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Null set
In set theory, a null set N \subset \mathbb is a set that can be covered by a countable union of intervals of arbitrarily small total length.
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Olga Oleinik
Olga Arsenievna Oleinik HFRSE (О́льга Арсе́ньевна Оле́йник) (2 July 1925 – 13 October 2001) was a Soviet mathematician who conducted pioneering work on the theory of partial differential equations, the theory of strongly inhomogeneous elastic media, and the mathematical theory of boundary layers.
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One-sided limit
In calculus, a one-sided limit is either of the two limits of a function f(x) of a real variable x as x approaches a specified point either from below or from above.
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Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
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Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
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Partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).
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Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
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Partition of an interval
In mathematics, a partition of an interval on the real line is a finite sequence of real numbers such that In other terms, a partition of a compact interval is a strictly increasing sequence of numbers (belonging to the interval itself) starting from the initial point of and arriving at the final point of.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Plane (geometry)
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
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Point (geometry)
In modern mathematics, a point refers usually to an element of some set called a space.
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Pointwise product
The pointwise product of two functions is another function, obtained by multiplying the image of the two functions at each value in the domain.
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Probability measure
In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity.
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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.
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Product rule
In calculus, the product rule is a formula used to find the derivatives of products of two or more functions.
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Radon measure
In mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff topological space X that is locally finite and inner regular.
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Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Reduced derivative
In mathematics, the reduced derivative is a generalization of the notion of derivative that is well-suited to the study of functions of bounded variation.
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Relative direction
The most common relative directions are left, right, forward(s), backward(s), up, and down.
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Relatively compact subspace
In mathematics, a relatively compact subspace (or relatively compact subset, or precompact subset) Y of a topological space X is a subset whose closure is compact.
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Renato Caccioppoli
Renato Caccioppoli (20 January 1904 – 8 May 1959) was an Italian mathematician, known for his contributions to mathematical analysis, including the theory of functions of several complex variables, functional analysis, measure theory.
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Riemann–Stieltjes integral
In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes.
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Riesz representation theorem
There are several well-known theorems in functional analysis known as the Riesz representation theorem.
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Riesz–Markov–Kakutani representation theorem
In mathematics, the Riesz–Markov–Kakutani representation theorem relates linear functionals on spaces of continuous functions on a locally compact space to measures.
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Russian Mathematical Surveys
Uspekhi Matematicheskikh Nauk (Успехи математических наук) is a Russian mathematical journal, published by the Russian Academy of Sciences and Moscow Mathematical Society and translated into English as Russian Mathematical Surveys.
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Scuola Normale Superiore di Pisa
The Scuola Normale Superiore di Pisa (SNS) is a public higher learning institution in Pisa, Italy.
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Semi-continuity
In mathematical analysis, semi-continuity (or semicontinuity) is a property of extended real-valued functions that is weaker than continuity.
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Separable space
In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Sigma-algebra
In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X that includes the empty subset, is closed under complement, and is closed under countable unions and countable intersections.
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Signed measure
In mathematics, signed measure is a generalization of the concept of measure by allowing it to have negative values.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Sobolev space
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of ''Lp''-norms of the function itself and its derivatives up to a given order.
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Space (mathematics)
In mathematics, a space is a set (sometimes called a universe) with some added structure.
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Spectral theory
In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces.
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Spectral theory of ordinary differential equations
In mathematics, the spectral theory of ordinary differential equations is the part of spectral theory concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential equation.
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Studia Mathematica
Studia Mathematica is a Polish mathematics journal published since 1929.
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Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
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Summation
In mathematics, summation (capital Greek sigma symbol: ∑) is the addition of a sequence of numbers; the result is their sum or total.
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Support (mathematics)
In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.
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Tony F. Chan
Tony Fan-Cheong Chan is a Hong Kong-born mathematician.
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Topological vector space
In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis.
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Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
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Total variation
In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure.
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Transactions of the American Mathematical Society
The Transactions of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.
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Uniform norm
In mathematical analysis, the uniform norm (or sup norm) assigns to real- or complex-valued bounded functions f defined on a set S the non-negative number This norm is also called the supremum norm, the Chebyshev norm, or the infinity norm. The name "uniform norm" derives from the fact that a sequence of functions \ converges to f under the metric derived from the uniform norm if and only if f_n converges to f uniformly.
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Unit vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.
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Variable (mathematics)
In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.
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Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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Vector-valued function
A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors.
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Władysław Orlicz
Władysław Roman Orlicz (May 24, 1903 in Okocim, Austria-Hungary (now Poland) – August 9, 1990 in Poznań, Poland) was a Polish mathematician of Lwów School of Mathematics.
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Weak derivative
In mathematics, a weak derivative is a generalization of the concept of the derivative of a function (strong derivative) for functions not assumed differentiable, but only integrable, i.e., to lie in the L''p'' space \mathrm^1().
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Weak solution
In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense.
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Weight function
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set.
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Young measure
In mathematical analysis, a Young measure is a parameterized measure that is associated with certain subsequences of a given bounded sequence of measurable functions.
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Redirects here:
BV function, Bv function, Bv space, Function of bounded variation, Function variation, SBV function, SBV functions.
References
[1] https://en.wikipedia.org/wiki/Bounded_variation
