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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 Kingman's subadditive ergodic theorem ： ウィキペディア英語版 Kingman's subadditive ergodic theorem In mathematics, Kingman's subadditive ergodic theorem is one of several ergodic theorems. It can be seen as a generalization of Birkhoff's ergodic theorem.〔S. Lalley, Kingman's subadditive ergodic theorem lecture notes, http://galton.uchicago.edu/~lalley/Courses/Graz/Kingman.pdf〕 Intuitively, the subadditive ergodic theorem is a kind of random variable version of Fekete's lemma (hence the name ergodic).〔http://math.nyu.edu/degree/undergrad/Chen.pdf〕 As a result, it can be rephrased in the language of probability, e.g. using a sequence of random variables and expected values. The theorem is named after John Kingman. ==Statement of theorem== Let $T$ be a measure-preserving transformation on the probability space $(\backslash Omega,\backslash Sigma,\backslash mu)$, and let $\backslash \_(x)\backslash le\; g\_n(x)+g\_m(T^nx)$ (subadditivity relation). Then : $\backslash lim\_\backslash frac=g(x)\backslash ge-\backslash infty$ for $\backslash mu$-a.e. ''x'', where ''g''(''x'') is ''T''-invariant. If ''T'' is ergodic, then ''g''(''x'') is a constant. 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「Kingman's subadditive ergodic 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.