Metrizability and paracompactness of probability measure spaces
Let \(P(X)\) be the family of probability measures on Tikhonov space \(X\) [\textit{V. V. Fedorchuk}, Russ. Math. Surv. 46, No. 1, 45-93 (1991); translation from Usp. Mat. Nauk 46, No. 1(227), 41-80 (1991; Zbl 0735.54033)]. The author proves that if \(X\) is metrizable, then \(P(X)\) is also metrizable. Furthermore, if \(X\) is \(p\)-paracompact, then \(P(X)\) is also \(p\)-paracompact. The author gives a characterization of absolute retracts of a metrizable space \(X\) in terms of some convex subsets of \(P(X)\).
scientific article; zbMATH DE number 732060
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