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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 Hewitt–Savage zero–one law ： ウィキペディア英語版 Hewitt–Savage zero–one law The Hewitt–Savage zero–one law is a theorem in probability theory, similar to Kolmogorov's zero–one law and the Borel–Cantelli lemma, that specifies that a certain type of event will either almost surely happen or almost surely not happen. It is sometimes known as the Hewitt–Savage law for symmetric events. It is named after Edwin Hewitt and Leonard Jimmie Savage. ==Statement of the Hewitt–Savage zero–one law== Let $(X\_n)\_^\backslash infty$ be a sequence of independent and identically-distributed random variables taking values in a set $\backslash mathbb$. The Hewitt–Savage zero–one law says that any event whose occurrence or non-occurrence is determined by the values of these random variables and whose occurrence or non-occurrence is unchanged by finite permutations of the indices, has probability either 0 or 1 (a "finite" permutation is one that leaves all but finitely many of the indices fixed). Somewhat more abstractly, define the ''exchangeable sigma algebra'' or ''sigma algebra of symmetric events'' $\backslash mathcal$ to be the set of events (depending on the sequence of variables $(X\_n)\_^\backslash infty$) which are invariant under finite permutations of the indices in the sequence $(X\_n)\_^\backslash infty$. Then $A\; \backslash in\; \backslash mathcal\; \backslash implies\; \backslash mathbb\; (A)\; \backslash in\; \backslash$. Since any finite permutation can be written as a product of transpositions, if we wish to check whether or not an event $A$ is symmetric (lies in $\backslash mathcal$), it is enough to check if its occurrence is unchanged by an arbitrary transposition $(i,\; j)$, $i,\; j\; \backslash in\; \backslash mathbb$. 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「Hewitt–Savage zero–one law」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.