Regular measure — In mathematics, a regular measure on a topological space is a measure for which every measurable set is approximately open and approximately closed .DefinitionLet ( X , T ) be a topological space and let Σ be a sigma; algebra on X that contains… … Wikipedia
Inner regular measure — In mathematics, an inner regular measure is one for which the measure of a set can be approximated from within by compact subsets.DefinitionLet ( X , T ) be a Hausdorff topological space and let Sigma; be a sigma; algebra on X that contains the… … Wikipedia
Uniformly distributed measure — In mathematics specifically, in geometric measure theory a uniformly distributed measure on a metric space is one for which the measure of an open ball depends only on its radius and not on its centre. By convention, the measure is also required… … Wikipedia
List of integration and measure theory topics — This is a list of integration and measure theory topics, by Wikipedia page.Intuitive foundations*Length *Area *Volume *Probability *Moving averageRiemann integral*Riemann sum *Riemann Stieltjes integral *Bounded variation *Jordan contentImproper… … Wikipedia
Borel measure — In mathematics, the Borel algebra is the smallest sigma; algebra on the real numbers R containing the intervals, and the Borel measure is the measure on this sigma; algebra which gives to the interval [ a , b ] the measure b − a (where a < b… … Wikipedia
Radon measure — In mathematics (specifically, measure theory), a Radon measure, named after Johann Radon, is a measure on the σ algebra of Borel sets of a Hausdorff topological space X that is locally finite and inner regular. Contents 1 Motivation 2 Definitions … Wikipedia
Haar measure — In mathematical analysis, the Haar measure is a way to assign an invariant volume to subsets of locally compact topological groups and subsequently define an integral for functions on those groups.This measure was introduced by Alfréd Haar, a… … Wikipedia
Trivial measure — In mathematics, specifically in measure theory, the trivial measure on any measurable space ( X , Σ) is the measure μ which assigns zero measure to every measurable set: μ ( A ) = 0 for all A in Σ.Properties of the trivial measureLet μ denote the … Wikipedia
Regularity theorem for Lebesgue measure — In mathematics, the regularity theorem for Lebesgue measure is a result in measure theory that states that Lebesgue measure on the real line is a regular measure. Informally speaking, this means that every Lebesgue measurable subset of the real… … Wikipedia
Dirac measure — In mathematics, a Dirac measure is a measure δx on a set X (with any σ algebra of subsets of X) defined by for a given and any (measurable) set A ⊆ X. The Dirac measure is a probability measure, and in terms of probability it represents … Wikipedia
