Definition 14.5.3 (Regular). Let $X$ be a topological space and $\mu: \cb_{X} \to [0, \infty]$ be a measure, then $\mu$ is regular if it is inner regular and outer regular on all Borel sets.
Definition 14.5.3 (Regular). Let $X$ be a topological space and $\mu: \cb_{X} \to [0, \infty]$ be a measure, then $\mu$ is regular if it is inner regular and outer regular on all Borel sets.