1.*8. In the case above, there exists an integrable function cp(., .) with the property that for each B E qjl, is cp(x, y) dy is a version of 2P{Y E B I X = x}. [This is called a "conditional density func tion in the wide sense" and

(x, TJ) = 1~ cp(x, y) dy is the corresponding conditional distribution in the wide sense:

(x, TJ) = gt>{Y < TJ I X = x}.

The term "wide sense" refers to the fact that these are functions on .9lI rather than on Q; see Doob [1, Sec. I.9].]