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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 Dirac measure ： ウィキペディア英語版 Dirac measure In mathematics, a Dirac measure assigns a size to a set based solely on whether it contains a fixed point ''x'' or not. It is one way of formalizing the idea of the Dirac delta function, an important tool in physics and engineering. ==Definition== A Dirac measure is a measure ''δ''''x'' on a set ''X'' (with any ''σ''-algebra of subsets of ''X'') defined for a given ''x'' ∈ ''X'' and any (measurable) set ''A'' ⊆ ''X'' by : where $1\_A$ is the indicator function of $A$. The Dirac measure is a probability measure, and in terms of probability it represents the almost sure outcome ''x'' in the sample space ''X''. We can also say that the measure is a single atom at ''x''; however, treating the Dirac measure as an atomic measure is not correct when we consider the sequential definition of Dirac delta, as the limit of a delta sequence. The Dirac measures are the extreme points of the convex set of probability measures on ''X''. The name is a back-formation from the Dirac delta function, considered as a Schwartz distribution, for example on the real line; measures can be taken to be a special kind of distribution. The identity :$\backslash int\_\; f(y)\; \backslash ,\; \backslash mathrm\; \backslash delta\_\; (y)\; =\; f(x),$ which, in the form :$\backslash int\_\; f(y)\; \backslash delta\_\; (y)\; \backslash ,\; \backslash mathrm\; y\; =\; f(x),$ is often taken to be part of the definition of the "delta function", holds as a theorem of Lebesgue integration. 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「Dirac measure」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.