I have an end of section problem from my analysis book that I would like a hint on, it reads: Prove that if are mutually disjoint measurable sets on the line then for any set A,

I have seen the proof for a finite number, n, of measurable sets where induction is used on n, could the same method be used and extended to the countably infinite case? Or should I be trying to show that the intersections of the E_k sets with A are measurable (regardless if A is measurable) and use the proposition stating the union of a countable collection of measurable sets is measurable then I can say the outer measure is equal to the lebesgue measure? I'm just not sure which direction I should take this, any suggestions?