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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 Tightness of measures ： ウィキペディア英語版 Tightness of measures In mathematics, tightness is a concept in measure theory. The intuitive idea is that a given collection of measures does not "escape to infinity." ==Definitions== Let $(X,\; T)$ be a topological space, and let $\backslash Sigma$ be a σ-algebra on $X$ that contains the topology $T$. (Thus, every open subset of $X$ is a measurable set and $\backslash Sigma$ is at least as fine as the Borel σ-algebra on $X$.) Let $M$ be a collection of (possibly signed or complex) measures defined on $\backslash Sigma$. The collection $M$ is called tight (or sometimes uniformly tight) if, for any $\backslash varepsilon\; >\; 0$, there is a compact subset $K\_$ of $X$ such that, for all measures $\backslash mu\; \backslash in\; M$, : where $|\backslash mu|$ is the total variation measure of $\backslash mu$. Very often, the measures in question are probability measures, so the last part can be written as :$\backslash mu\; (K\_)\; >\; 1\; -\; \backslash varepsilon.\; \backslash ,$ If a tight collection $M$ consists of a single measure $\backslash mu$, then (depending upon the author) $\backslash mu$ may either be said to be a tight measure or to be an inner regular measure. If $Y$ is an $X$-valued random variable whose probability distribution on $X$ is a tight measure then $Y$ is said to be a separable random variable or a Radon random variable. 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「Tightness of measures」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.