PlanetPhysics/Regular Measure

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 $$A' \in \mathcal{B}(X)$$ with $$A' \subset G - K$$, one has $$\mu_R(A') <\varepsilon$$.