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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 is the indicator function of . 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 : which, in the form : 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
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