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Izv. RAN. Ser. Mat., 1999, Volume 63, Issue 4, Pages 207–223 (Mi izv253)  

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

Bibliographic databases:

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. V. Sadovnichii, “On soft mappings of the unit ball of Borel measures”, J. Math. Sci., 136:5 (2006), 4156–4165  mathnet  crossref  mathscinet  zmath  elib  elib
    2. Sadovnichii Yu.V., “On topological and categorical properties of the functors M-tau and M-R”, Doklady Mathematics, 75:3 (2007), 349–352  crossref  mathscinet  zmath  isi  elib  scopus
    3. R. E. Zhiemuratov, A. A. Zaitov, “O veschestvennoi polnote prostranstva slabo additivnykh $\sigma$-gladkikh funktsionalov”, Vladikavk. matem. zhurn., 11:1 (2009), 22–28  mathnet  mathscinet  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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