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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 Monotone class theorem ： ウィキペディア英語版 Monotone class theorem In measure theory and probability, the monotone class theorem connects monotone classes and sigma-algebras. The theorem says that the smallest monotone class containing an algebra of sets G is precisely the smallest σ-algebra containing G. It is used as a type of transfinite induction to prove many other theorems, such as Fubini's theorem. ==Definition of a monotone class== A monotone class in a set $R$ is a collection $M$ of subsets of $R$ which contains $R$ and is closed under countable monotone unions and intersections, i.e. if $A\_i\; \backslash in\; M$ and $A\_1\; \backslash subset\; A\_2\; \backslash subset\; \backslash ldots$ then $\backslash cup\_^\backslash infty\; A\_i\; \backslash in\; M$, and similarly for intersections of decreasing sequences of sets. 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「Monotone class 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.