An analog of the Vitali-Hahn-Saks theorem

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.