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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 Maximum theorem ： ウィキペディア英語版 Maximum theorem The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers as a parameter changes. The statement was first proven by Claude Berge in 1959.〔Ok, p. 306〕 The theorem is primarily used in mathematical economics. ==Statement of theorem== Let $X$ and $\backslash Theta$ be metric spaces, $f:X\backslash times\backslash Theta\backslash to\backslash mathbb$ be a function jointly continuous in its two arguments, and $C:\backslash Theta\backslash twoheadrightarrow\; X$ be a compact-valued correspondence. For $x$ in $X$ and $\backslash theta$ in $\backslash Theta$, let : $f^$ *(\theta)=\max\ and : $C^$ *(\theta)=\mathrm\max\=\. If $C$ is continuous (i.e. both upper and lower hemicontinuous) at some $\backslash theta$, then $f^$ * is continuous at $\backslash theta$ and $C^$ * is non-empty, compact-valued, and upper hemicontinuous at $\backslash theta$. 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「Maximum 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.