outer regular


Let X be a locally compact Hausdorff topological space with Borel σ–algebra , and suppose μ is a measureMathworldPlanetmath on (X,). For any Borel set B, the measure μ is said to be outer regular on B if

μ(B)=inf{μ(U)UB,Uopen}.

We say μ is inner regular on B if

μ(B)=sup{μ(K)KB,Kcompact}.
Title outer regular
Canonical name OuterRegular
Date of creation 2013-03-22 12:39:57
Last modified on 2013-03-22 12:39:57
Owner djao (24)
Last modified by djao (24)
Numerical id 4
Author djao (24)
Entry type Definition
Classification msc 28A12
Related topic BorelSigmaAlgebra
Defines inner regular