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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 Fréchet–Kolmogorov theorem ： ウィキペディア英語版 Fréchet–Kolmogorov theorem In functional analysis, the Fréchet–Kolmogorov theorem (the names of Riesz or Weil are sometimes added as well) gives a necessary and sufficient condition for a set of functions to be relatively compact in an ''L''''p'' space. It can be thought of as an ''L''''p'' version of the Arzelà–Ascoli theorem, from which it can be deduced. The theorem is named after Maurice René Fréchet and Andrey Kolmogorov. == Statement == Let $B$ be a bounded set in $L^p(\backslash mathbb^n)$, with $p\backslash in[1,\backslash infty)$. The subset ''B'' is relatively compact if and only if the following properties hold: #$\backslash lim\_\backslash int\_\backslash left|f\backslash right|^p=0$ uniformly on ''B'', #$\backslash lim\_\backslash Vert\backslash tau\_a\; f-f\backslash Vert\_\; =\; 0$ uniformly on ''B'', where $\backslash tau\_a\; f$ denotes the translation of $f$ by $a$, that is, $\backslash tau\_a\; f(x)=f(x-a)\; .$ The second property can be stated as $\backslash forall\; \backslash varepsilon\; >0\; \backslash ,\; \backslash ,\; \backslash exists\; \backslash delta\; >0$ such that with 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「Fréchet–Kolmogorov 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.