regular measure

Definition 0.1.

A regular measure $\mu_{R}$ on a topological space $X$ is a measure on $X$ such that for each $A\in\mathcal{B}(X)$ , with $\mu_{R}(A)<\infty$ ), and each $\varepsilon>0$ there exist a compact subset $K$ of $X$ and an open subset $G$ of $X$ with $K\subset A\subset G$ , such that for all sets $A^{\prime}\in\mathcal{B}(X)$ with $A^{\prime}\subset G-K$ , one has $\mu_{R}(A^{\prime})<\varepsilon$ .

Title	regular measure
Canonical name	RegularMeasure
Date of creation	2013-03-22 18:23:07
Last modified on	2013-03-22 18:23:07
Owner	bci1 (20947)
Last modified by	bci1 (20947)
Numerical id	5
Author	bci1 (20947)
Entry type	Definition
Classification	msc 28C15
Classification	msc 28A12
Classification	msc 28A10
Related topic	OuterMeasure