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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 Unconditional convergence ： ウィキペディア英語版 Unconditional convergence Unconditional convergence is a topological property (convergence) related to an algebraical object (sum). It is an extension of the notion of convergence for series of countably many elements to series of arbitrarily many. It has been mostly studied in Banach spaces. == Definition == Let $X$ be a topological vector space. Let $I$ be an index set and $x\_i\; \backslash in\; X$ for all $i\; \backslash in\; I$. The series $\backslash textstyle\; \backslash sum\_\; x\_i$ is called unconditionally convergent to $x\; \backslash in\; X$, if * the indexing set $I\_0\; :=\backslash$ is countable and * for every permutation of $I\_0\; :=\backslash$ the relation holds:$\backslash sum\_^\backslash infty\; x\_i\; =\; x$ 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「Unconditional convergence」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.