Geodesic
An analog of the Vitali-Hahn-Saks theorem
Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 641-652.

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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. 
@article{MZM_1976_19_4_a18,
     author = {N. S. Gusel'nikov},
     title = {An analog of the {Vitali-Hahn-Saks} theorem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {641--652},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a18/}
}
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N. S. Gusel'nikov. An analog of the Vitali-Hahn-Saks theorem. Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 641-652. http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a18/