Measure Theory/Probability.

Solve the following:

(a) Let Pi and P2 be probability measures on the same measurable space (2, F). Suppose that there exists such a set-algebra A such that F = o(A). We say that P, and P2 are mutually singular with respect to each other if there exists H E F such that PI(H) = 1 and P2 (H) = 0. Show that Pi and P2 are mutually singular if and only if for every & > 0 there exists A E A such that PI(A) > 1 - E and P2(A)