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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 be a topological space, and let be a σ-algebra on that contains the topology . (Thus, every open subset of is a measurable set and is at least as fine as the Borel σ-algebra on .) Let be a collection of (possibly signed or complex) measures defined on . The collection is called tight (or sometimes uniformly tight) if, for any , there is a compact subset of such that, for all measures , : where is the total variation measure of . Very often, the measures in question are probability measures, so the last part can be written as : If a tight collection consists of a single measure , then (depending upon the author) may either be said to be a tight measure or to be an inner regular measure. If is an -valued random variable whose probability distribution on is a tight measure then 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
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