Let A Rn and let |A|e be the Lebesgue outer measure.
Suppose A, B Rn and d(A,B)>0. How do I prove that |A B|e=|A|e+|B|e?
Having thought about this problem for days, I still can't solve it. Any suggestion?
Hi, I would try this:
then there exists open set such that :
Since every open set in is Lebesgue measurable, there holds
Rewriting this for and using properties 1,2 of set seems to be a good way to solve your problem.