THE BROOKS-JEVETT THEOREM ON UNIFORM DIMENTRICULARITY ON A NON-SIGMA-FULL CLASS OF SETS



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Abstract

For a sequence of exhaustive composition-triangular set functions defined on a non-sigma-complete class of sets, more general than the ring of sets, the Brooks-Jewett theorem on uniform exhaustibility is proved. As a corollary, we have obtained analogue of the Brooks-Jewett theorem for functions defined on a sigma-summable class of sets. It is shown that if, in addition to the property compositional triangularity, the set functions have the composite semi-additivity property and are continuous from above at zero, then an analog of Nikodym’s theorem on equicontinuous weak continuity is valid for them. The corresponding results are obtained for a family of quasi-Lipschitz set functions.

About the authors

T. A. Sribnaya

Samara National Research University

Author for correspondence.
Email: morenov.sv@ssau.ru
Russian Federation

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