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Mat. Zametki, 1976, Volume 19, Issue 4, Pages 641–652 (Mi mz7784)  

This article is cited in 1 scientific paper (total in 1 paper)

An analog of the Vitali-Hahn-Saks theorem

N. S. Gusel'nikov

A. I. Hertsen Leningrad Pedagogical Institute

Abstract: This paper considers $N$-triangular $s$-bounded set functions. We prove for these functions a fairly close analog both of the Vitali–Hahn–Saks theorem and of the corresponding results of Brooks and Darst for finitely additive vector measures. As simple corollaries, we obtain various modifications of the Vitali–Hahn–Saks theorem for certain classes of additive and nonadditive scalar and vector-valued set functions.

Full text: PDF file (970 kB)

English version:
Mathematical Notes, 1976, 19:4, 387–392

Bibliographic databases:

UDC: 519.5
Received: 11.12.1974

Citation: N. S. Gusel'nikov, “An analog of the Vitali-Hahn-Saks theorem”, Mat. Zametki, 19:4 (1976), 641–652; Math. Notes, 19:4 (1976), 387–392

Citation in format AMSBIB
\Bibitem{Gus76}
\by N.~S.~Gusel'nikov
\paper An analog of the Vitali-Hahn-Saks theorem
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 4
\pages 641--652
\mathnet{http://mi.mathnet.ru/mz7784}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=419724}
\zmath{https://zbmath.org/?q=an:0334.28002}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 4
\pages 387--392
\crossref{https://doi.org/10.1007/BF01156804}


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    This publication is cited in the following articles:
    1. 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
  • Математические заметки Mathematical Notes
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