=+33.5. 1

(a) There is a slightly different approach to conditional probability. Let

(2, 5, P) be a probability space, (f', ') a measurable space, and 7' : (2 -+ 0'

a mapping measurable 9/ 9'. Define a measure > on 9' by v(A') = P(An)

T-'A') for A' € 9'. Prove that there exists a function p( Alo') on S', measur-

able "' and integrable PT-1, such that [ .. p( Alo')PT-'(do') = P(ANT"'A')