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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 Dini's theorem ： ウィキペディア英語版 Dini's theorem In the mathematical field of analysis, Dini's theorem says that if a monotone sequence of continuous functions converges on a compact space and if the limit function is also continuous, then the convergence is uniform. ==Formal statement== If ''X'' is a compact topological space, and is a monotonically increasing sequence (meaning for all ''n'' and ''x'') of continuous real-valued functions on ''X'' which converges pointwise to a continuous function ''f'', then the convergence is uniform. The same conclusion holds if is monotonically decreasing instead of increasing. The theorem is named after Ulisse Dini. This is one of the few situations in mathematics where pointwise convergence implies uniform convergence; the key is the greater control implied by the monotonicity. Note also that the limit function must be continuous, since a uniform limit of continuous functions is necessarily continuous. 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「Dini's 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.