11. If a statistic T is sufficient for 9, then for every function I which is

(d, Pu)-integrable for all 8 e n there exists a determination of the conditional expectation function Eu[f(X)lt] that is independent of 8. [If !I" is Euclidean, this follows from Theorems 5 and 7. In general, if I is nonnegative there exists a nondecreasing sequence of simple nonnegative functions In tending to I. Since the conditional expectation of a simple function can be taken to be independent of 8 by Lemma 3(i), the desired result follows from Lemma 3(iv).]