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This article is cited in 3 scientific papers (total in 3 papers)
Topological completeness of spaces of measures
V. V. Fedorchuk
M. V. Lomonosov Moscow State University
Abstract:
We prove that the functors $P_R$ and $P_\tau$ of Radon and $\tau$-additive probability measures, respectively, preserve neither the real-completeness nor the Dieudonne completeness of Tychonoff spaces. We suggest conditions under which Martin's axiom implies that $P_\tau$ preserves real-complete spaces, absolute extensors, and Tychonoff bundles. These last results cannot be obtained without additional set-theoretic assumptions.
DOI:
https://doi.org/10.4213/im253
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English version:
Izvestiya: Mathematics, 1999, 63:4, 827–843
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MSC: 54H99, 60B05, 28C15
Received: 25.12.1997
Citation:
V. V. Fedorchuk, “Topological completeness of spaces of measures”, Izv. RAN. Ser. Mat., 63:4 (1999), 207–223; Izv. Math., 63:4 (1999), 827–843
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/izv253https://doi.org/10.4213/im253 http://mi.mathnet.ru/eng/izv/v63/i4/p207
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This publication is cited in the following articles:
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Yu. V. Sadovnichii, “On soft mappings of the unit ball of Borel measures”, J. Math. Sci., 136:5 (2006), 4156–4165
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Sadovnichii Yu.V., “On topological and categorical properties of the functors M-tau and M-R”, Doklady Mathematics, 75:3 (2007), 349–352
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R. E. Zhiemuratov, A. A. Zaitov, “O veschestvennoi polnote prostranstva slabo additivnykh $\sigma$-gladkikh funktsionalov”, Vladikavk. matem. zhurn., 11:1 (2009), 22–28
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