Finitely Additive Conditional Probabilities, Conglomerability and Disintegrations

摘要: For any finitely additive probability measure to be disintegrable, that is, an average with respect some marginal distribution of a system conditional probabilities, it suffices, and is plainly necessary, the conglomerative, there expectation such no random variable can negative if variable's given each events nonnegative. With margins, partitions, are measures so far from being disintegrable they cannot approximated in total variation norm by those are. Those partitions which have this property determined. Many partially defined particular, all disintegrations, or, equivalently, strategies, restrictions full probabilities $Q = Q(A \mid B)$ for pairs $A$ $B$ non-null.