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35 relations: Absolute continuity, American Mathematical Monthly, American Mathematical Society, Banach space, Bernhard Riemann, Bounded variation, C0-semigroup, Cantor function, Classification of discontinuities, Cumulative distribution function, Darboux integral, Differentiable function, Directed set, Dual space, Expected value, Hölder condition, Improper integral, Integral, Integration by parts, Laplace–Stieltjes transform, Lebesgue integration, Lebesgue measure, Mathematics, Moment (mathematics), Net (mathematics), Partition of an interval, Probability density function, Probability distribution, Random variable, Real number, Rectifier (neural networks), Riemann integral, Spectral theorem, The Quarterly Journal of Pure and Applied Mathematics, Thomas Joannes Stieltjes.
Absolute continuity
In calculus, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity.
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American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
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American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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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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Bernhard Riemann
Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.
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Bounded variation
In mathematical analysis, a function of bounded variation, also known as function, is a real-valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense.
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C0-semigroup
In mathematics, a C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function.
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Cantor function
In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous.
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Classification of discontinuities
Continuous functions are of utmost importance in mathematics, functions and applications.
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Cumulative distribution function
In probability theory and statistics, the cumulative distribution function (CDF, also cumulative density function) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.
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Darboux integral
In real analysis, a branch of mathematics, the Darboux integral is constructed using Darboux sums and is one possible definition of the integral of a function.
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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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Directed set
In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set A together with a reflexive and transitive binary relation ≤ (that is, a preorder), with the additional property that every pair of elements has an upper bound.
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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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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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Hölder condition
In mathematics, a real or complex-valued function f on d-dimensional Euclidean space satisfies a Hölder condition, or is Hölder continuous, when there are nonnegative real constants C, α, such that for all x and y in the domain of f. More generally, the condition can be formulated for functions between any two metric spaces.
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Improper integral
In mathematical analysis, an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number, \infty, -\infty, or in some instances as both endpoints approach limits.
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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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Integration by parts
In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of their derivative and antiderivative.
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Laplace–Stieltjes transform
The Laplace–Stieltjes transform, named for Pierre-Simon Laplace and Thomas Joannes Stieltjes, is an integral transform similar to the Laplace transform.
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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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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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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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Net (mathematics)
In mathematics, more specifically in general topology and related branches, a net or Moore–Smith sequence is a generalization of the notion of a sequence.
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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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Probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.
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Probability distribution
In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
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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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Rectifier (neural networks)
In the context of artificial neural networks, the rectifier is an activation function defined as the positive part of its argument: f(x).
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Riemann integral
In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval.
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Spectral theorem
In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis).
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The Quarterly Journal of Pure and Applied Mathematics
The Quarterly Journal of Pure and Applied Mathematics was a mathematics journal that first appeared as such in 1855, but as the continuation of The Cambridge Mathematical Journal that had been launched in 1836 and had run in four volumes before changing its title to The Cambridge and Dublin Mathematical Journal for a further nine volumes (these latter volumes carried dual numbering).
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Thomas Joannes Stieltjes
Thomas Joannes Stieltjes (29 December 1856 – 31 December 1894) was a Dutch mathematician.
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References
[1] https://en.wikipedia.org/wiki/Riemann–Stieltjes_integral
