Inequalities for Ek(X, Y) when the marginals are fixed

Abstract

When k(x, y) is a quasi-monotone function and the random variables X and Y have fixed distributions, it is shown under some further mild conditions that ℰ k(X, Y) is a monotone functional of the joint distribution function of X and Y. Its infimum and supremum are both attained and correspond to explicitly described joint distribution functions. © 1976 Springer-Verlag.