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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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1  
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
3  
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

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