Several authors [1], [2], ⋯, [6], have derived characterizations of a conditional expectation operator. That is, if T is a transformation which maps a particular set of functions into the same set, ...

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 ...