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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Wiener–Wintner theorem ： ウィキペディア英語版 Wiener–Wintner theorem In mathematics, the Wiener–Wintner theorem, named after Norbert Wiener and Aurel Wintner, is a strengthening of the ergodic theorem, proved by ==Statement== Suppose that ''τ'' is a measure-preserving transformation of a measure space ''S'' with finite measure. If ''f'' is a real-valued integrable function on ''S'' then the Wiener–Wintner theorem states that there is a measure 0 set ''E'' such that the average :$\backslash lim\_\backslash frac\backslash sum\_^\backslash ell\; e^\; f(\backslash tau^j\; P)$ exists for all real λ and for all ''P'' not in ''E''. The special case for ''λ'' = 0 is essentially the Birkhoff ergodic theorem, from which the existence of a suitable measure 0 set ''E'' for any fixed ''λ'', or any countable set of values ''λ'', immediately follows. The point of the Wiener–Wintner theorem is that one can choose the measure 0 exceptional set ''E'' to be independent of ''λ''. This theorem was even much more generalized by the Return Times Theorem. 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「Wiener–Wintner theorem」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.