This article is cited 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.

UDC: 519.5

Received: 11.12.1974

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

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