Does anyone have a good proof of Littlewood's first principle?
Let $E$ be a measurable subset of $\mathbb{R}$ of finite measure, and let $\epsilon > 0$. Can anyone provide a rigorous proof that there is an open set $O$ which is the union of a finite number of pairwise disjoint open bounded intervals such that $m(O \setminus E) + m(E \setminus O) < \epsilon$.
Any references or answers would be greatly appreciated!