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Mat. Sb. (N.S.), 1978, Volume 106(148), Number 3(7), Pages 340–356 (Mi msb2579)  

This article is cited in 2 scientific papers (total in 2 papers)

Triangular set functions and Nikodým's theorem on the uniform boundedness of a family of measures

N. S. Gusel'nikov


Abstract: In this work triangular set functions are considered. Nikodým's theorem on the uniform boundedness of families of measures is generalized and simultaneously sharpened in a nontrivial way to these functions. As simple corollaries several generalizations of Nikodým's theorem are derived, which were obtained for additive vector-valued functions by Mikusiński, Drewnowski and others; the structural character of uniformly bounded families of triangular set functions is revealed.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Sbornik, 1979, 35:1, 19–33

Bibliographic databases:

UDC: 519.5
MSC: 28B10
Received: 20.09.1977

Citation: N. S. Gusel'nikov, “Triangular set functions and Nikodým's theorem on the uniform boundedness of a family of measures”, Mat. Sb. (N.S.), 106(148):3(7) (1978), 340–356; Math. USSR-Sb., 35:1 (1979), 19–33

Citation in format AMSBIB
\Bibitem{Gus78}
\by N.~S.~Gusel'nikov
\paper Triangular set functions and Nikod\'ym's theorem on the uniform boundedness of a~family of measures
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 106(148)
\issue 3(7)
\pages 340--356
\mathnet{http://mi.mathnet.ru/msb2579}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=507501}
\zmath{https://zbmath.org/?q=an:0418.28003|0387.28002}
\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 1
\pages 19--33
\crossref{https://doi.org/10.1070/SM1979v035n01ABEH001446}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JB17500002}


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  • http://mi.mathnet.ru/eng/msb/v148/i3/p340

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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, “Uniform boundedness of a family of nonadditive set functions”, Math. USSR-Sb., 66:2 (1990), 393–403  mathnet  crossref  mathscinet  zmath  isi
    2. N. S. Gusel'nikov, “Triangular set functions and the Nikodym, Brooks-Jewett, and Vitali-Hahn-Saks theorems on convergent sequences of measures”, Sb. Math., 202:6 (2011), 807–827  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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