Let Fi(x) and F2(y) be the distribution functions of two random variables. Frechet proved that the family of joint distributions having Fi(x) and F2(y) as marginal distributions collapses to F1(x)F2(y) if and only if either F,(x) or F2(y) is a unit step function. We rephrase his result in terms of abstract probability measures and with the aid of the above construction of doubly stochastic measures, we show his result is equivalent to the statement that Cartesian product measure is an extreme point of the set of doubly stochastic measures. 2. The construction. (X, S, A) and (Y, T, v) are two abstract probability triples. (X x Y, S x T) is the Cartesian cross product measure space of the measure spaces (X, S) and (Y, T). X is called a doubly stochastic measure on (X x Y, S x T) if X(A x Y) = ,u(A), for all A in S; X(X x B) = v(B), for all B in T. Cartesian product measure ,u x v is a doubly stochastic measure. THEOREM 1. Let { A i} and { Bj} be finite or countably infinite measurable partitions of X and Y, respectively, then the set function