PlanetMath: Borel measure

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Borel measure

(Definition)

Definition - Let be a topological space and $\mathcal{B}$ be its Borel $\sigma$ -algebra. A Borel measure on is a measure on the measurable space $(X,\mathcal{B})$ .

Remark - The restriction of the Lebesgue measure to the Borel $\sigma$ -algebra of $\mathbb{R}^n$ is also sometimes called “the” Borel measure of $\mathbb{R}^n$ .

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See Also: Borel $\sigma$ -algebra, Radon measure

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Cross-references: Lebesgue measure, measurable space, measure, topological space
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This is version 6 of Borel measure, born on 2007-10-01, modified 2008-04-12.
Object id is 9976, canonical name is BorelMeasure.
Accessed 1044 times total.

Classification:

AMS MSC:	28A10 (Measure and integration :: Classical measure theory :: Real- or complex-valued set functions)
	28A12 (Measure and integration :: Classical measure theory :: Contents, measures, outer measures, capacities)
	28C15 (Measure and integration :: Set functions and measures on spaces with additional structure :: Set functions and measures on topological spaces )
	60A10 (Probability theory and stochastic processes :: Foundations of probability theory :: Probabilistic measure theory)

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