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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2007, Volume 3, Number 2, Pages 196–212 (Mi jmag58)  

This article is cited in 9 scientific papers (total in 9 papers)

Dominated convergence and Egorov theorems for filter convergence

V. Kadets, A. Leonov

Department of Mechanics and Mathematics, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61077, Ukraine
Full-text PDF (321 kB) Citations (9)
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Abstract: We study the filters, such that for convergence with respect to this filters the Lebesgue dominated convergence theorem and the Egorov theorem on almost uniform convergence are valid (the Lebesgue filters and the Egorov filters, respectively). Some characterizations of the Egorov and the Lebesgue filters are given. It is shown that the class of Egorov filters is a proper subset of the class of Lebesgue filters, in particular, statistical convergence filter is the Lebesgue but not the Egorov filter. It is also shown that there are no free Lebesgue ultrafilters. Significant attention is paid to the filters generated by a matrix summability method.
Key words and phrases: measure theory, dominated convergence theorem, Egorov theorem, filter convergence, statistical convergence, matrix summability.
Received: 18.05.2006
Bibliographic databases:
Document Type: Article
MSC: 28A20, 54A20, 40C05
Language: English
Citation: V. Kadets, A. Leonov, “Dominated convergence and Egorov theorems for filter convergence”, Zh. Mat. Fiz. Anal. Geom., 3:2 (2007), 196–212
Citation in format AMSBIB
\Bibitem{KadLeo07}
\by V.~Kadets, A.~Leonov
\paper Dominated convergence and Egorov theorems for filter convergence
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2007
\vol 3
\issue 2
\pages 196--212
\mathnet{http://mi.mathnet.ru/jmag58}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2338187}
\zmath{https://zbmath.org/?q=an:1179.28007}
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  • This publication is cited in the following 9 articles:
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