Dominated Convergence and Egorov Theorems for Filter Convergen

Dominated Convergence and Egorov Theorems for Filter Convergen

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 fi...

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Published in:Журнал математической физики, анализа, геометрии
Date:2007
Main Authors: Kadets, V., Leonov, A.
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2007
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/106445
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Dominated Convergence and Egorov Theorems for Filter Convergen / V. Kadets, A. Leonov // Журнал математической физики, анализа, геометрии. — 2007. — Т. 3, № 2. — С. 196-212. — Бібліогр.: 11 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-106445
record_format dspace
spelling Kadets, V.
Leonov, A.
2016-09-28T19:02:31Z
2016-09-28T19:02:31Z
2007
Dominated Convergence and Egorov Theorems for Filter Convergen / V. Kadets, A. Leonov // Журнал математической физики, анализа, геометрии. — 2007. — Т. 3, № 2. — С. 196-212. — Бібліогр.: 11 назв. — англ.
1812-9471
https://nasplib.isofts.kiev.ua/handle/123456789/106445
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.
en
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
Журнал математической физики, анализа, геометрии
Dominated Convergence and Egorov Theorems for Filter Convergen
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Dominated Convergence and Egorov Theorems for Filter Convergen
spellingShingle Dominated Convergence and Egorov Theorems for Filter Convergen
Kadets, V.
Leonov, A.
title_short Dominated Convergence and Egorov Theorems for Filter Convergen
title_full Dominated Convergence and Egorov Theorems for Filter Convergen
title_fullStr Dominated Convergence and Egorov Theorems for Filter Convergen
title_full_unstemmed Dominated Convergence and Egorov Theorems for Filter Convergen
title_sort dominated convergence and egorov theorems for filter convergen
author Kadets, V.
Leonov, A.
author_facet Kadets, V.
Leonov, A.
publishDate 2007
language English
container_title Журнал математической физики, анализа, геометрии
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
format Article
description 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.
issn 1812-9471
url https://nasplib.isofts.kiev.ua/handle/123456789/106445
citation_txt Dominated Convergence and Egorov Theorems for Filter Convergen / V. Kadets, A. Leonov // Журнал математической физики, анализа, геометрии. — 2007. — Т. 3, № 2. — С. 196-212. — Бібліогр.: 11 назв. — англ.
work_keys_str_mv AT kadetsv dominatedconvergenceandegorovtheoremsforfilterconvergen
AT leonova dominatedconvergenceandegorovtheoremsforfilterconvergen
first_indexed 2025-12-07T15:46:27Z
last_indexed 2025-12-07T15:46:27Z
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