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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 compact convergence ： ウィキペディア英語版 compact convergence In mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence which generalizes the idea of uniform convergence. It is associated with the compact-open topology. ==Definition== Let $(X,\; \backslash mathcal)$ be a topological space and $(Y,d\_)$ be a metric space. A sequence of functions :$f\_\; :\; X\; \backslash to\; Y$, $n\; \backslash in\; \backslash mathbb,$ is said to converge compactly as $n\; \backslash to\; \backslash infty$ to some function $f\; :\; X\; \backslash to\; Y$ if, for every compact set $K\; \backslash subseteq\; X$, :$(f\_)|\_\; \backslash to\; f|\_$ converges uniformly on $K$ as $n\; \backslash to\; \backslash infty$. This means that for all compact $K\; \backslash subseteq\; X$, :$\backslash lim\_\; \backslash sup\_\; d\_\; \backslash left(\; f\_\; (x),\; f(x)\; \backslash right)\; =\; 0.$ 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「compact 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.