It is shown that the convergence in probability of random sets introduced by Salinetti and Wets is consistent with the more standard definitions of convergence in probability, and is metric invariant.
G. Salinetti, W. Vervaat, R. J.-B. Wets, (1986) On the Convergence in Probability of Random Sets (Measurable Multifunctions). Mathematics of Operations Research 11(3):420-422.
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