Outer regular measure
= Outer regular measure
{title2=$\mu(E)=\inf_{U\supseteq E,\ U\ {\rm open}}\mu(U)$}
= Outer regularity
{synonym}
A <measure> on a topological space is outer regular on its measurable sets when the displayed open-cover identity holds. <Lebesgue measure> has this property. It allows a null set to be placed in arbitrarily small open neighborhoods, and a compact small set to receive a smooth cutoff of similarly small integral.