Problem 3. Let (S, F, P) be a probability triple. Also assume that Bi E F with P(Bi) > 0 for all i E N. (a) Define P1 : F - [0, 1] as Pi(A) = P( A | B1 ) for all A E F. Prove that Pl is a probability measure on . (b) For any given integer n 2 2, define Pn(A) = Pn-1( A | Bn ) for all A E F where P1 is defined in part (a). Find (identify) the limiting measure Q = limn > Pn where Q(A) = limn +co Pn(A) for A E F, if it exists. Also clarify the condition under which this limiting measure exists