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Mat. Zametki, 1997, Volume 62, Issue 1, Pages 103–110 (Mi mz1592)  

This article is cited in 5 scientific papers (total in 5 papers)

Convergence of a sequence of weakly regular set functions

V. M. Klimkin, T. A. Sribnaya

Samara State University

Abstract: The present paper is devoted to generalizations of the Dieudonné theorem claiming that the convergence of sequences of regular Borelian measures is preserved under the passage from a system of open subsets of a compact metric space to the class of all Borelian subsets of this space. The Dieudonné theorem is proved in the case for which the set functions are weakly regular, nonadditive, defined on an algebra of sets that contains the class of open subsets of an arbitrary $\sigma$-topological space, and take values in a uniform space.

DOI: https://doi.org/10.4213/mzm1592

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English version:
Mathematical Notes, 1997, 62:1, 87–92

Bibliographic databases:

UDC: 517
Received: 07.02.1995

Citation: V. M. Klimkin, T. A. Sribnaya, “Convergence of a sequence of weakly regular set functions”, Mat. Zametki, 62:1 (1997), 103–110; Math. Notes, 62:1 (1997), 87–92

Citation in format AMSBIB
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\by V.~M.~Klimkin, T.~A.~Sribnaya
\paper Convergence of a sequence of weakly regular set functions
\jour Mat. Zametki
\yr 1997
\vol 62
\issue 1
\pages 103--110
\mathnet{http://mi.mathnet.ru/mz1592}
\crossref{https://doi.org/10.4213/mzm1592}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1619992}
\zmath{https://zbmath.org/?q=an:0947.28004}
\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 1
\pages 87--92
\crossref{https://doi.org/10.1007/BF02356068}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000071268600011}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. M. Klimkin, T. A. Sribnaya, “Uniform Continuity of a Family of Weakly Regular Set Functions on Topological Spaces”, Math. Notes, 74:1 (2003), 56–63  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Cavaliere, P, “On Brooks-Jewett, Vitali-Hahn-Saks and Nikodym convergence theorems for quasi-triangular functions”, Rendiconti Lincei-Matematica E Applicazioni, 20:4 (2009), 387  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Ventriglia F., “Dieudonne's theorem for non-additive set functions”, Journal of Mathematical Analysis and Applications, 367:1 (2010), 296–303  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Cavaliere P., de Lucia P., Ventriglia F., “On Drewnowski lemma for non-additive functions and its consequences”, Positivity, 14:1 (2010), 1–16  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. Cavaliere P. de Lucia P. De Simone A. Ventriglia F., “On the Lebesgue Decomposition For Non-Additive Functions”, Positivity, 18:3 (2014), 489–503  crossref  mathscinet  zmath  isi  scopus  scopus
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