# 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 RegularMeasure 2013-03-22 18:23:07 2013-03-22 18:23:07 bci1 (20947) bci1 (20947) 5 bci1 (20947) Definition msc 28C15 msc 28A12 msc 28A10 OuterMeasure