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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 Continuous mapping theorem ： ウィキペディア英語版 Continuous mapping theorem In probability theory, the continuous mapping theorem states that continuous functions are limit-preserving even if their arguments are sequences of random variables. A continuous function, in Heine’s definition, is such a function that maps convergent sequences into convergent sequences: if ''xn'' → ''x'' then ''g''(''xn'') → ''g''(''x''). The ''continuous mapping theorem'' states that this will also be true if we replace the deterministic sequence with a sequence of random variables , and replace the standard notion of convergence of real numbers “→” with one of the types of convergence of random variables. This theorem was first proved by , and it is therefore sometimes called the Mann–Wald theorem. ==Statement== Let , ''X'' be random elements defined on a metric space ''S''. Suppose a function (where ''S′'' is another metric space) has the set of discontinuity points ''Dg'' such that . Then # $X\_n\; \backslash \; \backslash xrightarrow\backslash \; X\; \backslash quad\backslash Rightarrow\backslash quad\; g(X\_n)\backslash \; \backslash xrightarrow\backslash \; g(X);$ # $X\_n\; \backslash \; \backslash xrightarrow\backslash \; X\; \backslash quad\backslash Rightarrow\backslash quad\; g(X\_n)\backslash \; \backslash xrightarrow\backslash \; g(X);$ # $X\_n\; \backslash \; \backslash xrightarrow\backslash \; X\; \backslash quad\backslash Rightarrow\backslash quad\; g(X\_n)\backslash \; \backslash xrightarrow\backslash \; g(X).$ 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「Continuous mapping 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.