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An analog of the Vitali-Hahn-Saks theorem

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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.

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Authors and Affiliations

  1. Leningrad State Pedagogical Institute, USSR

    N. S. Gusel'nikov

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  1. N. S. Gusel'nikov
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Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 641–652, April, 1976.

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Gusel'nikov, N.S. An analog of the Vitali-Hahn-Saks theorem. Mathematical Notes of the Academy of Sciences of the USSR 19, 387–392 (1976). https://doi.org/10.1007/BF01156804

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  • DOI: https://doi.org/10.1007/BF01156804

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