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



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