This question has come up while playing around with the Steinhaus theorem:
Let $F-F$ denote the algebraic difference $\{f-g \mod 1 | f,g \in F\}$. Suppose that $F\subset[0,1]$ with $\mu F>0$ , where $\mu$ is the usual Lebesgue measure. If we know that $F-F = [0,1]$, may we conclude that $\mu F = 1$?
Thanks for your input!