In probability, if we have a space (S, M, P) with probability measure P, and a measurable function : N R, we call the integral f fdP the expected value of f. Similarly, the conditional probability of an event f(x) A given f(x) B is defined by P(f = A) = P{x N: f(x) = An B} P{TEN: f(x) = B} Use the Radon Nikodym theorem to construct a meaningful notion of the expected value of given fe B.