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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 Fraňková–Helly selection theorem ： ウィキペディア英語版 Fraňková–Helly selection theorem In mathematics, the Fraňková–Helly selection theorem is a generalisation of Helly's selection theorem for functions of bounded variation to the case of regulated functions. It was proved in 1991 by the Czech mathematician Dana Fraňková. ==Background== Let ''X'' be a separable Hilbert space, and let BV((''T'' ); ''X'') denote the normed vector space of all functions ''f'' : (''T'' ) → ''X'' with finite total variation over the interval (''T'' ), equipped with the total variation norm. It is well known that BV((''T'' ); ''X'') satisfies the compactness theorem known as Helly's selection theorem: given any sequence of functions (''f''''n'')''n''∈N in BV((''T'' ); ''X'') that is uniformly bounded in the total variation norm, there exists a subsequence :$\backslash left(\; f\_\; \backslash right)\; \backslash subseteq\; (f\_)\; \backslash subset\; \backslash mathrm((T);\; X)$ and a limit function ''f'' ∈ BV((''T'' ); ''X'') such that ''f''''n''(''k'')(''t'') converges weakly in ''X'' to ''f''(''t'') for every ''t'' ∈ (''T'' ). That is, for every continuous linear functional ''λ'' ∈ ''X'' *, :$\backslash lambda\; \backslash left(\; f\_(t)\; \backslash right)\; \backslash to\; \backslash lambda(f(t))\; \backslash mbox\; \backslash mathbb\; \backslash mbox\; k\; \backslash to\; \backslash infty.$ Consider now the Banach space Reg((''T'' ); ''X'') of all regulated functions ''f'' : (''T'' ) → ''X'', equipped with the supremum norm. Helly's theorem does not hold for the space Reg((''T'' ); ''X''): a counterexample is given by the sequence :$f\_\; (t)\; =\; \backslash sin\; (n\; t).$ One may ask, however, if a weaker selection theorem is true, and the Fraňková–Helly selection theorem is such a result. 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「Fraňková–Helly selection 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.