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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 Kolmogorov's three-series theorem ： ウィキペディア英語版 Kolmogorov's three-series theorem In probability theory, Kolmogorov's Three-Series Theorem, named after Andrey Kolmogorov, gives a criterion for the almost sure convergence of an infinite series of random variables in terms of the convergence of three different series involving properties of their probability distributions. Kolmogorov's three-series theorem, combined with Kronecker's lemma, can be used to give a relatively easy proof of the Strong Law of Large Numbers.〔Durrett, Rick. "Probability: Theory and Examples." Duxbury advanced series, Third Edition, Thomson Brooks/Cole, 2005, Section 1.8, pp. 60–69.〕 == Statement of the theorem == Let (''X''''n'')''n''∈N be independent random variables. The random series ∑∞''n''=1''X''''n'' converges almost surely in ℝ if and only if the following conditions hold for some A > 0: i. ∑∞n=19px(|X|n ≥ A) converges ii. Let Yn:= Xn1, then ∑∞n=1E(Yn), the series of expected values of Yn , converges iii. ∑∞n=1var(Yn) converges 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「Kolmogorov's three-series 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.