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48 relations: Acta Mathematica, Almost all, Almost everywhere, American Mathematical Society, Analytic number theory, Benford's law, Borel measure, Complex-valued function, Compositio Mathematica, Darboux integral, Dimension, Diophantine approximation, Dirac delta function, Equidistribution theorem, Erdős–Turán inequality, Exponential sum, Fractional part, Geometric series, Graduate Studies in Mathematics, Hermann Weyl, Indicator function, Interval (mathematics), Ivan Vinogradov, Johannes van der Corput, Lebesgue integration, Lebesgue measure, Limit superior and limit inferior, Linear combination, Low-discrepancy sequence, Lp space, Mathematics, Mathematische Annalen, Metrization theorem, Monte Carlo integration, Pisot–Vijayaraghavan number, Prime number, Probability measure, Q.E.D., Real number, Riemann integral, Riemann sum, Separable space, Sigma-algebra, Springer Science+Business Media, Step function, Stone–Weierstrass theorem, Trigonometric polynomial, Van der Corput sequence.
Acta Mathematica
Acta Mathematica is a peer-reviewed open-access scientific journal covering research in all fields of mathematics.
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Almost all
In mathematics, the term "almost all" means "all but a negligible amount".
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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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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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Analytic number theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.
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Benford's law
Benford's law, also called Newcomb-Benford's law, law of anomalous numbers, and first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data.
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Borel measure
In mathematics, specifically in measure theory, a Borel measure on a topological space is a measure that is defined on all open sets (and thus on all Borel sets).
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Complex-valued function
In mathematics, a complex-valued function (not to be confused with complex variable function) is a function whose values are complex numbers.
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Compositio Mathematica
Compositio Mathematica is a bimonthly peer-reviewed mathematics journal established by L.E.J. Brouwer in 1935.
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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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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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Diophantine approximation
In number theory, the field of Diophantine approximation deals with the approximation of real numbers by rational numbers.
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Dirac delta function
In mathematics, the Dirac delta function (function) is a generalized function or distribution introduced by the physicist Paul Dirac.
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Equidistribution theorem
In mathematics, the equidistribution theorem is the statement that the sequence is uniformly distributed on the circle \mathbb/\mathbb, when a is an irrational number.
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Erdős–Turán inequality
In mathematics, the Erdős–Turán inequality bounds the distance between a probability measure on the circle and the Lebesgue measure, in terms of Fourier coefficients.
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Exponential sum
In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function Therefore, a typical exponential sum may take the form summed over a finite sequence of real numbers xn.
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Fractional part
The fractional part or decimal part of a non‐negative real number x is the excess beyond that number's integer part.
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Geometric series
In mathematics, a geometric series is a series with a constant ratio between successive terms.
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Graduate Studies in Mathematics
Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society (AMS).
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Hermann Weyl
Hermann Klaus Hugo Weyl, (9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher.
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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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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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Ivan Vinogradov
Ivan Matveevich Vinogradov (a; 14 September 1891 – 20 March 1983) (not to be confused with Askold Ivanovich Vinogradov of the Bombieri-Vinogradov theorem) was a Soviet mathematician, who was one of the creators of modern analytic number theory, and also a dominant figure in mathematics in the USSR.
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Johannes van der Corput
Johannes Gaultherus van der Corput (4 September 1890 – 16 September 1975) was a Dutch mathematician, working in the field of analytic number 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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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 combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
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Low-discrepancy sequence
In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of N, its subsequence x1,..., xN has a low discrepancy.
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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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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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Mathematische Annalen
Mathematische Annalen (abbreviated as Math. Ann. or, formerly, Math. Annal.) is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann.
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Metrization theorem
In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space.
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Monte Carlo integration
In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers.
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Pisot–Vijayaraghavan number
In mathematics, a Pisot–Vijayaraghavan number, also called simply a Pisot number or a PV number, is a real algebraic integer greater than 1 all of whose Galois conjugates are less than 1 in absolute value.
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Prime number
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
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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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Q.E.D.
Q.E.D. (also written QED and QED) is an initialism of the Latin phrase quod erat demonstrandum meaning "what was to be demonstrated" or "what was to be shown." Some may also use a less direct translation instead: "thus it has been demonstrated." Traditionally, the phrase is placed in its abbreviated form at the end of a mathematical proof or philosophical argument when the original proposition has been restated exactly, as the conclusion of the demonstration or completion of the proof.
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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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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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Riemann sum
In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum.
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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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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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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Step function
In mathematics, a function on the real numbers is called a step function (or staircase function) if it can be written as a finite linear combination of indicator functions of intervals.
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Stone–Weierstrass theorem
In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval can be uniformly approximated as closely as desired by a polynomial function.
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Trigonometric polynomial
In the mathematical subfields of numerical analysis and mathematical analysis, a trigonometric polynomial is a finite linear combination of functions sin(nx) and cos(nx) with n taking on the values of one or more natural numbers.
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Van der Corput sequence
A van der Corput sequence is an example of the simplest one-dimensional low-discrepancy sequence over the unit interval; it was first described in 1935 by the Dutch mathematician J. G. van der Corput.
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Discrepancy of a sequence, Equidistributed, Equidistributed mod 1, Equidistributed modulo 1, Equidistribution, Equidistribution mod 1, Equidistribution modulo 1, Equirepartioned sequence, Uniform distribution mod 1, Uniform distribution modulo 1, Uniformly distributed mod 1, Uniformly distributed modulo 1, Van der Corput set, Van der Corput theorem, Van der Corput's theorem, Well distributed sequence, Well-distributed sequence, Weyl criterion, Weyl criterion for equidistribution, Weyl equidistribution criterion, Weyl equidistribution theorem, Weyl s equidistribution criterion, Weyl's criterion, Weyl's criterion for equidistribution, Weyl's equidistribution criterion.
References
[1] https://en.wikipedia.org/wiki/Equidistributed_sequence
