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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 Sion's minimax theorem ： ウィキペディア英語版 Sion's minimax theorem In mathematics, and in particular game theory, Sion's minimax theorem is a generalization of John von Neumann's minimax theorem, named after Maurice Sion. It states: Let $X$ be a compact convex subset of a linear topological space and $Y$ a convex subset of a linear topological space. If $f$ is a real-valued function on $X\backslash times\; Y$ with : $f(x,\backslash cdot)$ upper semicontinuous and quasiconcave on $Y$, $\backslash forall\; x\backslash in\; X$, and : $f(\backslash cdot,y)$ lower semicontinuous and quasi-convex on $X$, $\backslash forall\; y\backslash in\; Y$ then, : $\backslash min\_\backslash sup\_\; f(x,y)=\backslash sup\_\backslash min\_f(x,y).$ ==See also== *Parthasarathy's theorem *Saddle point 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「Sion's minimax 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.