19.6.2.9 Measurable functions and sets

Problem: Prove that the set \( A \) will be measurable if for any number \( \varepsilon>0 \) such an open set \( B_{\varepsilon} \) will be found, that \( A \subset B_{\varepsilon} \) and \( \mu^{*}\left(B_{\varepsilon} \backslash A\right)<\varepsilon \).