PlanetPhysics/Regular Measure

A regular measure ${\mu }_R$ on a [[../CoIntersections/|topological]] space $X$ is a measure on $X$ such that for each $A\in ℬ(X)$ , with ${\mu }_R(A)<\mathrm{\infty }$), 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 ${\mu }_R(A^{\prime })<\epsilon$.