翻訳と辞書 Words near each other ・ Erechthias molynta ・ Erechthias mystacinella ・ Erdős–Kac theorem ・ Erdős–Ko–Rado theorem ・ Erdős–Mordell inequality ・ Erdős–Nagy theorem ・ Erdős–Nicolas number ・ Erdős–Pósa theorem ・ Erdős–Rado theorem ・ Erdős–Rényi model ・ Erdős–Stone theorem ・ Erdős–Straus conjecture ・ Erdős–Szekeres theorem ・ Erdős–Szemerédi theorem ・ Erdős–Turán conjecture on additive bases ・ Erdős–Turán inequality ・ Erdős–Woods number ・ Erdőtarcsa ・ ERE ・ ERE Informatique ・ Ere Kokkonen ・ Ere language ・ Ere. Elamvazhuthi ・ Ereal ・ ERealty ・ Erean Mountains ・ Erebabraxas ・ Erebango ・ Erebato River ・ Erebegraafplaats Bloemendaal Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Erdős–Turán inequality ： ウィキペディア英語版 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. It was proved by Paul Erdős and Pál Turán in 1948. Let ''μ'' be a probability measure on the unit circle R/Z. The Erdős–Turán inequality states that, for any natural number ''n'', :$\backslash sup\_A\; \backslash left|\; \backslash mu(A)\; -\; \backslash mathrm\backslash ,\; A\; \backslash right|$ \leq C \left( \frac + \sum_^n \frac \right), where the supremum is over all arcs ''A'' ⊂ R/Z of the unit circle, ''mes'' stands for the Lebesgue measure, :$\backslash hat(k)\; =\; \backslash int\; \backslash exp(2\; \backslash pi\; i\; k\; \backslash theta)\; \backslash ,\; d\backslash mu(\backslash theta)$ are the Fourier coefficients of μ, and ''C'' > 0 is a numerical constant. ==Application to discrepancy== Let ''s''1, ''s''2, ''s''3 ... ∈ R be a sequence. The Erdős–Turán inequality applied to the measure :$\backslash mu\_m(S)\; =\; \backslash frac\; \backslash \#\; \backslash ,\; \backslash quad\; S\; \backslash subset\; [0,\; 1),$ yields the following bound for the discrepancy: :$$ \begin D(m) & \left( = \sup_ \Big| m^ \# \ - (b-a) \Big| \right) \\[8pt] & \leq C \left( \frac + \frac \sum_^n \frac \left| \sum_^m e^ \right|\right). \end \qquad (1) This inequality holds for arbitrary natural numbers ''m,n'', and gives a quantitative form of Weyl's criterion for equidistribution. A multi-dimensional variant of (1) is known as the Erdős–Turán–Koksma inequality. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Erdős–Turán inequality」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.