For every Lebesgue measurable set $E \subset \mathbb{R}^n$, [Lebesgue measure](/page/Lebesgue%20Measure) is outer regular on $E$. If $\mathcal{L}^n(E)<\infty$, then Lebesgue measure is inner regular on $E$. Moreover, if $\mathcal{L}^n(E)<\infty$, then for every $\varepsilon>0$ there are an [open set](/page/Open%20Set) $U \subset \mathbb{R}^n$ and a compact set $K \subset \mathbb{R}^n$ such that \begin{align*} K \subset E \subset U, \qquad \mathcal{L}^n(U \setminus K) < \varepsilon. \end{align*}