Abstract
This chapter presents the Kolmogorov consistency theorem and conditional probability. The general setting in which one attempts to solve the problem of existence of random variables with preassigned joint distributions involves the notion of standard Borel spaces. A countably generated Borel space (X, B) is called standard if there exists a complete separable metric space Y such that the σ-algebras B and BY are σ-isomorphic. The chapter also presents a study of the properties of standard Borel spaces. The conditional probability of any set A ε B given that π(x) = y is given by P (A ∩ Xy)/P (Xy).
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