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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