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 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?