# Approximating bounded measurable sets by compact sets from the inside: reference needed

Does anyone know a precise reference on the following assertion? (The question has already been discussed here.)

Let $m$ denote the Lebesgue measure, and let $A\subset \mathbb{R}^d$ be $m$-measurable and bounded. Then, for every $\varepsilon>0$ there is a compact set $K_{\varepsilon}\subset A$ such that $m(A\setminus K_{\varepsilon})<\varepsilon$.