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.
A question about positive Lebesgue measure
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real-analysis
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1What about $F=[0,1]$ and $Q=\mathbb Q$? – 2011-08-12
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0$F$ might be a nowhere dense set. – 2011-08-12
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0I can't. answer the question. it's as difficult as the oringal question for me. – 2011-08-12
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3Hint: Lebesgue density theorem. – 2011-08-12
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0choose an $x\in F$ with density 1 , and so on? – 2011-08-12
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0Yes, 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