# A question about positive Lebesgue measure

Let $F$ be a set of reals of positive Lebesgue measure . Does there exist a countable $Q$,$F+Q$ almost cover $R$ in the sense of measure.

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What about $F=[0,1]$ and $Q=\mathbb Q$? –  Asaf Karagila Aug 12 '11 at 4:53
$F$ might be a nowhere dense set. –  Leitingok Aug 12 '11 at 4:55
I can't. answer the question. it's as difficult as the oringal question for me. –  Leitingok Aug 12 '11 at 5:12
Hint: Lebesgue density theorem. –  Zarrax Aug 12 '11 at 5:21
choose an $x\in F$ with density 1 , and so on? –  Leitingok Aug 12 '11 at 6:48