Convergence results for conditional expectations

Abstract

Let E, F be two Polish spaces and [Xn, Yn], [X, Y] random variables with values in E × F (not necessarily defined on the same probability space). We show some conditions which are sufficient in order to assure that, for each bounded continuous function f on E × F, the conditional expectation of f(Xn, Yn) given Yn converges in distribution to the conditional expectation of f(X, Y) given Y. © 2005 ISI/BS.