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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 Random compact set ： ウィキペディア英語版 Random compact set In mathematics, a random compact set is essentially a compact set-valued random variable. Random compact sets are useful in the study of attractors for random dynamical systems. ==Definition== Let $(M,\; d)$ be a complete separable metric space. Let $\backslash mathcal$ denote the set of all compact subsets of $M$. The Hausdorff metric $h$ on $\backslash mathcal$ is defined by :$h(K\_,\; K\_)\; :=\; \backslash max\; \backslash left\backslash \}\; d(a,\; b),\; \backslash sup\_\}\; d(a,\; b)\; \backslash right\backslash \}.$ $(\backslash mathcal,\; h)$ is also а complete separable metric space. The corresponding open subsets generate a σ-algebra on $\backslash mathcal$, the Borel sigma algebra $\backslash mathcal(\backslash mathcal)$ of $\backslash mathcal$. A random compact set is а measurable function $K$ from а probability space $(\backslash Omega,\; \backslash mathcal,\; \backslash mathbb)$ into $(\backslash mathcal,\; \backslash mathcal\; (\backslash mathcal)\; )$. Put another way, a random compact set is a measurable function $K\; \backslash colon\; \backslash Omega\; \backslash to\; 2^$ such that $K(\backslash omega)$ is almost surely compact and :$\backslash omega\; \backslash mapsto\; \backslash inf\_\; d(x,\; b)$ is a measurable function for every $x\; \backslash in\; M$. 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「Random compact set」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.