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Mat. Zametki, 1975, Volume 17, Issue 1, Pages 21–31 (Mi mz7219)  

This article is cited in 6 scientific papers (total in 6 papers)

Extension of quasi-Lipschitz set functions

N. S. Gusel'nikov

Leningrad State Pedagogical Institute, USSR

Abstract: In this article we consider so-called $\mathscr N$-triangular and quasi-Lipschitz set functions. In terms of $\mathscr N$ -semimeasures, we establish necessary and sufficient conditions for extending a quasi-Lipschitz set function which is continuous from above at zero from a ring of sets to the $\sigma$-ring generated by these sets, and also conditions for the uniqueness of the extension. As simple corollaries we obtain analogous results for vector-valued measures, continuous triangular measures, and real-valued finite $\mathscr N$ -triangular set functions which are continuous from above at zero.

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English version:
Mathematical Notes, 1975, 17:1, 14–19

Bibliographic databases:

UDC: 517.51:519.5
Received: 23.07.1973

Citation: N. S. Gusel'nikov, “Extension of quasi-Lipschitz set functions”, Mat. Zametki, 17:1 (1975), 21–31; Math. Notes, 17:1 (1975), 14–19

Citation in format AMSBIB
\Bibitem{Gus75}
\by N.~S.~Gusel'nikov
\paper Extension of quasi-Lipschitz set functions
\jour Mat. Zametki
\yr 1975
\vol 17
\issue 1
\pages 21--31
\mathnet{http://mi.mathnet.ru/mz7219}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=374376}
\zmath{https://zbmath.org/?q=an:0355.28001}
\transl
\jour Math. Notes
\yr 1975
\vol 17
\issue 1
\pages 14--19
\crossref{https://doi.org/10.1007/BF01093835}


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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. N. S. Gusel'nikov, “Triangular set functions and Nikodým's theorem on the uniform boundedness of a family of measures”, Math. USSR-Sb., 35:1 (1979), 19–33  mathnet  crossref  mathscinet  zmath  isi
    2. V. M. Klimkin, T. A. Sribnaya, “Convergence of a sequence of weakly regular set functions”, Math. Notes, 62:1 (1997), 87–92  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. 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
    4. Guselnikov N.S., “Ob usloviyakh edinstvennosti plotnogo prodolzheniya kvazilipshetsevykh funktsii mnozhestva”, Vestnik ishimskogo gosudarstvennogo pedagogicheskogo instituta im. P.P. Ershova, 2012, no. 6, 28–35  elib
    5. T. A. Sribnaya, “O prodolzhenii neadditivnykh funktsii mnozhestva”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 3, 34–40  mathnet  crossref  elib
    6. T. A. Sribnaya, “Teorema Bruksa–Dzhevetta o ravnomernoi ischerpyvaemosti na ne-sigma-polnom klasse mnozhestv”, Vestn. SamU. Estestvennonauchn. ser., 2017, no. 4, 33–39  mathnet  crossref  elib
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