1.*9. Let B be a Borel set, f 1 (x, B) -P(x, B), and define f n for n 2: 2 inductively by f n (x, B) = [ P(x, dy)f n-1 (y, B);

put f(x, B) -2::::0=1 f n(X, B). Prove that f(Xn, B) is a version of the conditional probability 9ft Jj n+1 [Xi E Bl I Xn} for the homogeneous Markov process with transition probability function Pc., .).