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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 Concentration dimension ： ウィキペディア英語版 Concentration dimension In mathematics — specifically, in probability theory — the concentration dimension of a Banach space-valued random variable is a numerical measure of how “spread out” the random variable is compared to the norm on the space. ==Definition== Let (''B'', || ||) be a Banach space and let ''X'' be a Gaussian random variable taking values in ''B''. That is, for every linear functional ''ℓ'' in the dual space ''B''∗, the real-valued random variable ⟨''ℓ'', ''X''⟩ has a normal distribution. Define :$\backslash sigma(X)\; =\; \backslash sup\; \backslash left\backslash \; )\}\; \backslash ,\backslash right|\backslash ,\; \backslash ell\; \backslash in\; B^,\; \backslash |\; \backslash ell\; \backslash |\; \backslash leq\; 1\; \backslash right\backslash \}.$ Then the concentration dimension ''d''(''X'') of ''X'' is defined by :$d(X)\; =\; \backslash frac\; )\}\{\backslash sigma(X)^\{2\}\}.$ 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「Concentration dimension」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.