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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 Talagrand's concentration inequality ： ウィキペディア英語版 Talagrand's concentration inequality In probability theory, Talagrand's concentration inequality is an isoperimetric-type inequality for product probability spaces. It was first proved by the French mathematician Michel Talagrand. The inequality is one of the manifestations of the concentration of measure phenomenon.〔 ==Statement== The inequality states that if $\backslash Omega\; =\; \backslash Omega\_1\; \backslash times\; \backslash Omega\_2\; \backslash times\; \backslash cdots\; \backslash times\; \backslash Omega\_n$ is a product space endowed with a product probability measure and $A$ is a subset in this space, then for any $t\; \backslash ge\; 0$ : $\backslash Pr()\; \backslash cdot\; \backslash Pr\backslash left()\; \backslash le\; e^\; \backslash ,\; ,$ where $\backslash overline$ is the complement of ''At'' where this is defined by :$A\_t\; =\; \backslash$ and where $\backslash rho$ is Talagrand's convex distance defined as : $\backslash rho(A,x)\; =\; \backslash max\_\; \backslash \; \backslash min\_\; \backslash \; \backslash sum\_\; \backslash alpha\_i$ where $\backslash alpha\; \backslash in\; \backslash mathbf^n$, $x,y\; \backslash in\; \backslash Omega$ are $n$-dimensional vectors with entries $\backslash alpha\_i,\; x\_i,\; y\_i$ respectively and $\backslash |\backslash cdot\backslash |\_2$ is the $\backslash ell^2$-norm. That is, :$\backslash |\backslash alpha\backslash |\_2=\backslash left(\backslash sum\_i\backslash alpha\_i^2\backslash right)^$ 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「Talagrand's concentration inequality」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.