The original problem is as follows:(adsbygoogle = window.adsbygoogle || []).push({});

IF E,F are measurable subset of R

and m(E),m(F)>0

then the set E+F contains interval.

After several hours of thought, I finally arrived at conclusion that

If I can show that m((E+c) [itex]\bigcap[/itex] F) is nonzero for some c in R,

then done.

But such a proposition(actually seems trivial...) is very hard to prove.

Could you give me some ideas for solving it?

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# Sum of sets with positive measure contains interval

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