I have problem here which I am having difficulty proving:
Assume that is a sequence of disjoint (Lebesgue) measurable sets, and A is any set. w.t.s.:
I have a proof of the finite case as i goes from 1 to n by using induction, however, it requires me to take the intersection of the last term in the sequence, which does not apply to the infinite case.
Also, I believe that is trivial since sub-additivity applies to the outer measure, and .
So, it may only be neccessary to prove it going the other way.
Thanks a million!