This article is cited in 2 papers

Triangular set functions and Nikodým's theorem on the uniform boundedness of a family of measures

N. S. Gusel'nikov


Abstract: In this work triangular set functions are considered. Nikodým's theorem on the uniform boundedness of families of measures is generalized and simultaneously sharpened in a nontrivial way to these functions. As simple corollaries several generalizations of Nikodým's theorem are derived, which were obtained for additive vector-valued functions by Mikusiński, Drewnowski and others; the structural character of uniformly bounded families of triangular set functions is revealed.
Bibliography: 10 titles.

UDC: 519.5

MSC: 28B10

Received: 20.09.1977

 English version: Mathematics of the USSR-Sbornik, 1979, 35:1, 19–33

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