A Consistency Theorem for Regular Conditional Distributions
نویسندگان
چکیده
Let (Ω,B) be a measurable space, An ⊂ B a sub-σ-field and μn a random probability measure on (Ω,B), n ≥ 1. In various frameworks, one looks for a probability P on B such that μn is a regular conditional distribution for P given An for all n. Conditions for such a P to exist are given. The conditions are quite simple when (Ω,B) is a compact Hausdorff space equipped with the Borel or the Baire σ-field (as well as under similar assumptions). Applications to Gibbs measures and Bayesian statistics are given as well.
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تاریخ انتشار 2004