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  1. H

    Sum of sets with positive measure contains interval

    hmm.. I think E+F = all irrationals between 0 and 2 is not right. 1.9 = pi/4 + (1.9- pi/4)
  2. H

    Sum of sets with positive measure contains interval

    The original problem is as follows: 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) \bigcap F) is nonzero for some c in R, then done. But such a...
  3. H

    Sum of two closed sets are measurable

    I got it. Thank you very much!
  4. H

    Sum of two closed sets are measurable

    hmm.. I'm not sure It is actually true that every seq in A+B has a convergent subseq. assuring the exsitence of conv subseq in A and B does not implies so as well A+B... Isn't it?
  5. H

    Sum of two closed sets are measurable

    Aha. I got your idea! I'm now wondering how I can show the fact that compactness is closed under the set addition.. Is it better to use open covering argument?
  6. H

    Sum of two closed sets are measurable

    hmm.. I thought that if A,B is closed, then A+B is not necessarily closed...
  7. H

    Sum of two closed sets are measurable

    I tried very long time to show that For closed subset A,B of R^d, A+B is measurable. A little bit of hint says that it's better to show that A+B is F-simga set... It seems also difficult for me as well... Could you give some ideas for problems?
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