m(A {intersection} U {1 to infinity} Ei)=Sum {1 to infinity} m(A {intersection} Ei)

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!