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This paper deals with three major types of convergence of probabilitymeasures on metric spaces: weak convergence, setwise converges, and convergencein the total variation. First, it describes and compares necessary andsufficient conditions for these types of convergence, some of which arewell-known, in terms of convergence of probabilities of open and closed setsand, for the probabilities on the real line, in terms of convergence ofdistribution functions. Second, it provides % convenient criteria for weak andsetwise convergence of probability measures and continuity of stochastickernels in terms of convergence of probabilities defined on the base of thetopology generated by the metric. Third, it provides applications to control ofPartially Observable Markov Decision Processes and, in particular, to MarkovDecision Models with incomplete information.

Convergence of Probability Measures and Markov Decision Models with Incomplete Information