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Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, Issue 4, Pages 33–39 (Mi vsgu560)  

Mathematics

The Brooks–Jevett theorem on uniform dimentricularity on a non-sigma-full class of sets

T. A. Sribnaya

Samara National Research University, 34, Moskovskoye shosse, Samara, 443086, Russian Federation

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.

Keywords: composition-triangular set functions, composition-semi-additive set functions, non-sigmacomplete class of sets, multiplicative class of sets, exhaustibility, continuity from above at zero, uniform exhaustibility, equicontinuous weak continuity.

DOI: https://doi.org/10.18287/2541-7525-2017-23-4-33-39

Full text: PDF file (222 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

UDC: 517.987
Received: 22.11.2017

Citation: T. A. Sribnaya, “The Brooks–Jevett theorem on uniform dimentricularity on a non-sigma-full class of sets”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, no. 4, 33–39

Citation in format AMSBIB
\Bibitem{Sri17}
\by T.~A.~Sribnaya
\paper The Brooks--Jevett theorem on uniform dimentricularity on a non-sigma-full class of sets
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2017
\issue 4
\pages 33--39
\mathnet{http://mi.mathnet.ru/vsgu560}
\crossref{https://doi.org/10.18287/2541-7525-2017-23-4-33-39}
\elib{https://elibrary.ru/item.asp?id=32274178}


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