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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 Gaussian isoperimetric inequality ： ウィキペディア英語版 Gaussian isoperimetric inequality In mathematics, the Gaussian isoperimetric inequality, proved by Boris Tsirelson and Vladimir Sudakov and independently by Christer Borell, states that among all sets of given Gaussian measure in the ''n''-dimensional Euclidean space, half-spaces have the minimal Gaussian boundary measure. == Mathematical formulation == Let $\backslash scriptstyle\; A$ be a measurable subset of $\backslash scriptstyle\backslash mathbf^n$ endowed with the Gaussian measure γ ''n''. Denote by : $A\_\backslash varepsilon\; =\; \backslash left\backslash (x,\; A)\; \backslash leq\; \backslash varepsilon\; \backslash right\backslash \}$ the ε-extension of ''A''. Then the ''Gaussian isoperimetric inequality'' states that : $\backslash liminf\_$ \varepsilon^ \left\ \geq \varphi(\Phi^(\gamma^n(A))), where : $\backslash varphi(t)\; =\; \backslash frac\backslash quad\backslash Phi(t)\; =\; \backslash int\_^t\; \backslash varphi(s)\backslash ,\; ds.$ 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「Gaussian isoperimetric 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.