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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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    What about $F=[0,1]$ and $Q=\mathbb Q$?2011-08-12
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    $F$ might be a nowhere dense set.2011-08-12
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    I can't. answer the question. it's as difficult as the oringal question for me.2011-08-12
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    Hint: Lebesgue density theorem.2011-08-12
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    choose an $x\in F$ with density 1 , and so on?2011-08-12
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    Yes, choose $x \in F$ with density $1$, let $Q = \mathbb Q$, and show $F+Q$ has full measure. Can you do that?2011-08-12

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