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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 Γ-convergence ： ウィキペディア英語版 Γ-convergence In the calculus of variations, Γ-convergence (Gamma-convergence) is a notion of convergence for functionals. It was introduced by Ennio de Giorgi. ==Definition== Let $X$ be a topological space and $F\_n:X\backslash to[0,+\backslash infty)$ a sequence of functionals on $X$. Then $F\_n$ are said to $\backslash Gamma$-converge to the $\backslash Gamma$-limit $F:X\backslash to[0,+\backslash infty)$ if the following two conditions hold: * Lower bound inequality: For every sequence $x\_n\backslash in\; X$ such that $x\_n\backslash to\; x$ as $n\backslash to+\backslash infty$, : $F(x)\backslash le\backslash liminf\_\; F\_n(x\_n).$ * Upper bound inequality: For every $x\backslash in\; X$, there is a sequence $x\_n$ converging to $x$ such that : $F(x)\backslash ge\backslash limsup\_\; F\_n(x\_n)$ The first condition means that $F$ provides an asymptotic common lower bound for the $F\_n$. The second condition means that this lower bound is optimal. 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「Γ-convergence」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.