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.
(2006) Almost sure weak convergence of random probability measures, Stochastics, 78, 91-97
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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.