measurable subset of nonmeasurable set

Question

show that if E is measurable and E⊂P where P is nonmeasurable set in [0,1), then m(E)=0.

Can one please tell how to start ..

and I have one more question: is the union of m'ble set and non-m'ble set m'ble? why?

(I think the union of m'ble set and non-m'ble set is non-m'ble set .but suppose P:=(E:=[0,1/2))∪(non measurable set in [1/2,1)) is non-m'ble however, E⊂P is measurable s.t m(E)≠0)

Answer 1

Let $P$ be a non-measurable subset of the real axis $R$. The following conditions are equivalent:

(i) for each measurable subset $E \subset P$ the condition $m(E)=0$ holds;

(ii) the inner $m$ measure of $P$ is equal to zero.