Characterization of Discrete Random Vectors by Conditional Expectations

For given real and monotone functionshiʹs, we obtain the necessary and sufficient conditions in order that any Rn-valuated functionΨ(x) be the conditional expectationE(h(X)/X>x) of a discrete random vectorX, whereh(X) denotes the random vector (h1(X1), …, hn(Xn)).