Convergence in probability of all predictive distributions of a sequence is characterized by stable convergence, setwise convergence of marginals, and a second-moment matching condition.
(1985) Exchangeability and related topics, Ecole d’et´ e de Probabilit´ es de Saint- Flour XIII, Lecture Notes in Math
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Weak convergence of predictive distributions
Convergence in probability of all predictive distributions of a sequence is characterized by stable convergence, setwise convergence of marginals, and a second-moment matching condition.