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

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.