翻訳と辞書 Words near each other ・ Vitaliy Sobko ・ Vitaliy Sobolev ・ Vitaliy Starukhin ・ Vitaliy Trukshin ・ Vitaliy Trushev ・ Vitaliy Tsykunov ・ Vitaliy Tymofiyenko ・ Vitaliy Vergeles ・ Vitaliy Vernydub ・ Vitaliy Vitsenets ・ Vitaliy Vizaver ・ Vitaliy Zakharchenko ・ Vitaliy Zheludok ・ Vitalization ・ Vitalize! ・ Vitali–Carathéodory theorem ・ Vitali–Hahn–Saks theorem ・ Vitaljina ・ Vitallium ・ Vitalogy ・ Vitalogy Tour ・ Vitals (Mutemath album) ・ Vitals (novel) ・ Vitals (website) ・ Vitaly (Ustinov) ・ Vitaly Abalakov ・ Vitaly Anikeyenko ・ Vitaly Anosov ・ Vitaly Arkhangelsky ・ Vitaly Atyushov Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Vitali–Carathéodory theorem ： ウィキペディア英語版 Vitali–Carathéodory theorem In mathematics, the Vitali–Carathéodory theorem is a result in real analysis that shows that, under the conditions stated below, integrable functions can be approximated in L1 from above and below by lower- and upper-semicontinuous functions, respectively. It is named after Giuseppe Vitali and Constantin Carathéodory. ==Statement of the theorem== Let ''X'' be a locally compact Hausdorff space equipped with a Borel measure, µ, that is finite on every compact set, outer regular, and tight when restricted to any Borel set that is open or of finite mass. If ''f'' is an element of L1(µ) then, for every ''ε'' > 0, there are functions ''u'' and ''v'' on ''X'' such that ''u'' ≤ ''f'' ≤ ''v'', ''u'' is upper-semicontinuous and bounded above, ''v'' is lower-semicontinuous and bounded below, and :$$ \int_X (v - u) \,\mathrm\mu < \varepsilon. 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「Vitali–Carathéodory 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.