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  1. 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...
  2. 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?