In probability, if we have a space (S, M, P) with probability measure P, and a...

    

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In probability, if we have a space (S, M, P) with probability measure P, and a measurable function ƒ : 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 ƒ given fe B. In probability, if we have a space (S, M, P) with probability measure P, and a measurable function ƒ : 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 ƒ given fe B.