Recent content by hhj5575

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

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...

I got it. Thank you very much!

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?

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?

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

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?