Let $E$ be a measurable subset of $R$ of positive lebesgue measure. Define the set $K$ by $K = {s + t: s \in E, t \in E}$
Prove that $K$ has nonempty interior.
I tried to prove it by contradiction. By measurability we can assume that $E$ is contained in an open set and with difference of measure at most $ε$. But I only can find countably many points not in this open set and can't conclude a contradiction.
