regular measure

Definition 0.1.

A regular measure ${\mu }_R$ on a topological space $X$ is a measure on $X$ such thatfor each $A\in ℬ(X)$ , with ), and each $\epsilon >0$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 $A^{\prime }\in ℬ(X)$ with $A^{\prime }\subset G-K$, one has .