Definition 5.4.1: Inner Regular

Definition 5.4.1 (Inner Regular).label Let $X$ be a topological space, $\mu:\cali{B}_{X}\to [0,\infty]$ be a Borel measure, and $E\in\cali{B}_{X}$ then $\mu$ is inner regular on $E$ if

\begin{align*}\mu(E)=\sup\curl{\mu(K):K\suf E,K\text{ compact}}\end{align*}