Corrections and hints for Assignment 9: PROBLEM 2b: Find an integrable function f such that d(T#m) = f(x) dm . (The function f is called the "density" of the measure t#m with respect to m). PROBLEM 5: Change the name of the set from "E" to "A" throughout, to avoid notational collision. Assume that all spaces X, X1, X2 are probability spaces, i.e., their total measure is 1. (The difficulty is that (X,N,nu) need not be sigma-finite, even if (X,M,\mu) is. Alternately, we could assume directly that both M and N are sigma-finite.) Part (b) In the definition of N, it should say "A element of M" (not "subset"). Part (c) Several typos. It should read "X1 cross X2" and "M_1 tensor {0,X2}" .