Let (Ω, F, P) be a probability space, and let X be a random variable defined on (Ω, F, P). If A is a sub σ-field of F, then E(X ∣ A) is the a.s. unique A measurable function such that, for all A ε A, ...
For any finitely additive probability measure to be disintegrable, that is, to be an average with respect to some marginal distribution of a system of finitely additive conditional probabilities, it ...
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