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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 Fubini's theorem on differentiation ： ウィキペディア英語版 Fubini's theorem on differentiation In mathematics, Fubini's theorem on differentiation, named after Guido Fubini, is a result in real analysis concerning the differentiation of series of monotonic functions. It can be proven by using Fatou's lemma and the properties of null sets.〔Jones, Frank (2001), ''Lebesgue Integration on Euclidean Space'', Jones and Bartlett publishers, pp. 527–529.〕 == Statement == Assume $I\; \backslash subseteq\; \backslash mathbb\; R$ is an interval and that for every natural number k, $f\_k:\; I\; \backslash to\; \backslash mathbb\; R$ is an increasing function. If, :$s(x)\; :=\; \backslash sum\_^\backslash infty\; f\_k(x)$ exists for all $x\; \backslash in\; I,$ then, :$s\text{'}(x)\; =\; \backslash sum\_^\backslash infty\; f\_k\text{'}(x)$ almost everywhere in ''I''.〔 In general, if we don't suppose fk is increasing for every k, in order to get the same conclusion, we need a stricter condition like uniform convergence of $\backslash sum\_^n\; f\_k\text{'}(x)$ on ''I'' for every n.〔Rudin, Walter (1976), ''Principles of Mathematical Analysis'', McGraw-Hill, p. 152.〕 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「Fubini's theorem on differentiation」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.