This is from a book which supposed to help you prepare for entrance exam. I am currently on a chapter regarding construction of measure and Caratheodory theory. I am having quite a hard time understanding the information part, this is one of the exercises in the section.
Let $m$ be the Lebesgue measure and A a Lebesgue measurable subset of $\mathbb{R}$ with $m(A)< \infty$. Let $\epsilon>0$. Show there exists $G$ open and $F$ closed such that $F\subset A\subset G$ and $m(G-F)<\epsilon$.