Hi there,

Suppose I have a sequence of probability measures P_n which converges weakly to a probability measure P. Then we know that \lim_{n} P_n (A)  = P(A) if A is a P-continuity set.
Is it true that if, in addition we know that each P_n and P are absolutely continuous, then \lim_{n} P_n (A) = P(A) for any A?

Thank you very much,