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44 relations: Almost everywhere, Cambridge University Press, Cartesian product, Cauchy–Schwarz inequality, Clarkson's inequalities, Complex conjugate, Complex number, Conditional expectation, Counting measure, Dual space, Equivalence class, Essential supremum and essential infimum, Euclidean space, Expected value, Function (mathematics), Harmonic mean, Hilbert space, Indicator function, Inequality (mathematics), Inner product space, Jensen's inequality, Lebesgue integration, Lebesgue measure, Linear independence, Lp space, Mathematical analysis, Mathematical induction, Measurable function, Measure space, Messenger of Mathematics, Minkowski inequality, Moment (mathematics), Norm (mathematics), Normed vector space, Otto Hölder, Probability space, Product measure, Random variable, Real number, Riesz–Thorin theorem, Sequence space, Sigma-algebra, Triangle inequality, Young's inequality for products.
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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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Cartesian product
In set theory (and, usually, in other parts of mathematics), a Cartesian product is a mathematical operation that returns a set (or product set or simply product) from multiple sets.
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Cauchy–Schwarz inequality
In mathematics, the Cauchy–Schwarz inequality, also known as the Cauchy–Bunyakovsky–Schwarz inequality, is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, vector algebra and other areas.
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Clarkson's inequalities
In mathematics, Clarkson's inequalities, named after James A. Clarkson, are results in the theory of ''L''''p'' spaces.
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Complex conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
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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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Conditional expectation
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value – the value it would take “on average” over an arbitrarily large number of occurrences – given that a certain set of "conditions" is known to occur.
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Counting measure
In mathematics, the counting measure is an intuitive way to put a measure on any set: the "size" of a subset is taken to be: the number of elements in the subset if the subset has finitely many elements, and ∞ if the subset is infinite.
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Dual space
In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V, together with the vector space structure of pointwise addition and scalar multiplication by constants.
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Equivalence class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.
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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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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Expected value
In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.
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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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Harmonic mean
In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the Pythagorean means.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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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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Inequality (mathematics)
In mathematics, an inequality is a relation that holds between two values when they are different (see also: equality).
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Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
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Jensen's inequality
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.
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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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Linear independence
In the theory of vector spaces, a set of vectors is said to be if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be.
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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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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 induction
Mathematical induction is a mathematical proof technique.
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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 space
A measure space is a basic object of measure theory, a branch of mathematics that studies generalized notions of volumes.
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Messenger of Mathematics
The Messenger of Mathematics is a defunct mathematics journal.
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Minkowski inequality
In mathematical analysis, the Minkowski inequality establishes that the L''p'' spaces are normed vector spaces.
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Moment (mathematics)
In mathematics, a moment is a specific quantitative measure, used in both mechanics and statistics, of the shape of a set of points.
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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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Otto Hölder
Otto Ludwig Hölder (December 22, 1859 – August 29, 1937) was a German mathematician born in Stuttgart.
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Probability space
In probability theory, a probability space or a probability triple (\Omega, \mathcal, P) is a mathematical construct that models a real-world process (or “experiment”) consisting of states that occur randomly.
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Product measure
In mathematics, given two measurable spaces and measures on them, one can obtain a product measurable space and a product measure on that space.
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Random variable
In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.
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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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Riesz–Thorin theorem
In mathematics, the Riesz–Thorin theorem, often referred to as the Riesz–Thorin interpolation theorem or the Riesz–Thorin convexity theorem is a result about interpolation of operators.
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Sequence space
In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers.
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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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Triangle inequality
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
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Young's inequality for products
In mathematics, Young's inequality for products is a mathematical inequality about the product of two numbers.
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References
[1] https://en.wikipedia.org/wiki/Hölder's_inequality
