Definition 5.4.2 (Outer 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 outer regular on $E$ if
\begin{align*}\mu(E)=\inf\curl{\mu(U):U\in\cali{N}^o(A)}\end{align*}
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