THE BROOKS-JEVETT THEOREM ON UNIFORM DIMENTRICULARITY ON A NON-SIGMA-FULL CLASS OF SETS
- Authors: Sribnaya T.A.1
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Affiliations:
- Samara National Research University
- Issue: Vol 23, No 4 (2017)
- Pages: 33-39
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/5710
- DOI: https://doi.org/10.18287/2541-7525-2017-23-4-33-39
- ID: 5710
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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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