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THE BROOKS-JEVETT THEOREM ON UNIFORM DIMENTRICULARITY ON A NON-SIGMA-FULL CLASS OF SETS
- Authors: Sribnaya T.A.1
-
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
References
- Dunford N., Schwartz J. Lineinye operatory. Obshchaia teoriia . М.: IIL, 1962, 896 p. .
- Brooks J.K., Jewett R.S. On finitely additive vector measures. Proc. Nat. Acad. Sci USA, 1970, Vol. 67, no 3, pp. 1294–1298 .
- Guselnikov N.S. O teoremakh Bruksa-Dzhevetta i Nikodima . In: Sb. Teoriia funktsii i funkts. analiz . L., 1975, pp. 45–54 .
- Klimkin V.M. Vvedenie v teoriiu funktsii mnozhestva . Izdatel’stvo Saratovskogo universiteta, Kuibyshevskii filial, 1989, 210 p. .
- Molto A. On the Vitali-Hahn-Saks theorem. Proc. Royal. Soc.. Edinburgh, 1981, Sect. A90, pp. 163–173 .
- Schachermayer W. On some classical measure-theoretic theorems for non-sigma-complete Boolean algebras. Dissertationes Math.. Warszawa, 1982, Vol. 214, pp. 1–33 .
- Friniche F.I. The Vitali-Hahn-Saks theorem for Boolean algebras with the subsequential interprolation property. Proc. Amer. Math. Soc., 1984, Vol. 92, no 3, pp. 362–366 .
- Lucia P., Marales P. Some Consequences of the Brooks-Jewett theorem for Additive Uniform Semigroup-valued Functions. Conf. Semin. Mat. Univ.. Bari, 1988, Vol. 227, pp. 1–23 .
- Guselnikov N.S. O prodolzhenii kvazilipshitsevykh funktsii mnozhestva . Matem. zametki , 1975, Vol. 17, no. 1, pp. 21–31 .
- Seever G.L. Measures on F-spaces. Trans. Amer. Math. Soc., 1968, Vol. 133, pp. 267–280 .
- Sribnaya T.A. Kriterii ravnomernoi ischerpyvaemosti semeistva vektornykh vneshnikh mer . Vestnik Samarskogo gosuniversiteta. Estestvennonauchnaia seriia , 2012, no 6 (97), pp. 58–65 .
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