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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 Almost convergent sequence ： ウィキペディア英語版 Almost convergent sequence A bounded real sequence $(x\_n)$ is said to be ''almost convergent'' to $L$ if each Banach limit assigns the same value $L$ to the sequence $(x\_n)$. Lorentz proved that $(x\_n)$ is almost convergent if and only if :$\backslash lim\backslash limits\_\; \backslash frac\}p=L$ uniformly in $n$. The above limit can be rewritten in detail as : Almost convergence is studied in summability theory. It is an example of a summability method which cannot be represented as a matrix method. ==References== * G. Bennett and N.J. Kalton: "Consistency theorems for almost convergence." Trans. Amer. Math. Soc., 198:23--43, 1974. * J. Boos: "Classical and modern methods in summability." Oxford University Press, New York, 2000. * J. Connor and K.-G. Grosse-Erdmann: "Sequential definitions of continuity for real functions." Rocky Mt. J. Math., 33(1):93--121, 2003. * G.G. Lorentz: "A contribution to the theory of divergent sequences." Acta Math., 80:167--190, 1948. 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「Almost convergent sequence」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.