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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 Helly–Bray theorem ： ウィキペディア英語版 Helly–Bray theorem In probability theory, the Helly–Bray theorem relates the weak convergence of cumulative distribution functions to the convergence of expectations of certain measurable functions. It is named after Eduard Helly and Hubert Evelyn Bray. Let ''F'' and ''F''1, ''F''2, ... be cumulative distribution functions on the real line. The Helly–Bray theorem states that if ''F''''n'' converges weakly to ''F'', then ::$\backslash int\_\backslash mathbb\; g(x)\backslash ,dF\_n(x)\; \backslash quad\backslash xrightarrow()\backslash quad\; \backslash int\_S\; g\; \backslash ,dP,$ for all bounded, continuous and real-valued functions on ''S''. (The integrals in this version of the theorem are Lebesgue–Stieltjes integrals.) The more general theorem above is sometimes taken as ''defining'' weak convergence of measures (see Billingsley, 1999, p. 3). ==References== # 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「Helly–Bray 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.