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Dirac MeasureIn mathematics, a Dirac measure is a measure δx on a set X that gives a given element x measure 1, so that - δx({x}) = 1
and in general - δx(Y) = 0
for any subset Y of X not containing x, - δx(Z) = 1
for any subset Z containing x. 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. 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.
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