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Equidistribution theorem

In mathematics, the equidistribution theorem is the statement that the sequence

is uniformly distributed on the circle , when a is an irrational number. It is a special case of the ergodic theorem where one takes the normalized angle measure .

Diophantine approximation

Low-discrepancy sequence

Dirichlet's approximation theorem

Three-gap theorem

P. Bohl, (1909) Über ein in der Theorie der säkularen Störungen vorkommendes Problem, J. reine angew. Math. 135, pp. 189–283.

Weyl, H. (1910). . Rendiconti del Circolo Matematico di Palermo. 330: 377–407. doi:10.1007/bf03014883. S2CID 122545523.

"Über die Gibbs'sche Erscheinung und verwandte Konvergenzphänomene"

W. Sierpinski, (1910) Sur la valeur asymptotique d'une certaine somme, Bull Intl. Acad. Polonaise des Sci. et des Lettres (Cracovie) series A, pp. 9–11.

Weyl, H. (1916). . Math. Ann. 77 (3): 313–352. doi:10.1007/BF01475864. S2CID 123470919.

"Ueber die Gleichverteilung von Zahlen mod. Eins"

Birkhoff, G. D. (1931). . Proc. Natl. Acad. Sci. U.S.A. 17 (12): 656–660. Bibcode:1931PNAS...17..656B. doi:10.1073/pnas.17.12.656. PMC 1076138. PMID 16577406.

"Proof of the ergodic theorem"

Ya. Khinchin, A. (1933). "Zur Birkhoff's Lösung des Ergodensproblems". Math. Ann. 107: 485–488. :10.1007/BF01448905. S2CID 122289068.

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