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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| Veröffentlicht in: | Журнал математической физики, анализа, геометрии |
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| Datum: | 2007 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2007
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/106445 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862680341783773184 |
|---|---|
| author | Kadets, V. Leonov, A. |
| author_facet | Kadets, V. Leonov, A. |
| 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| 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.
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| first_indexed | 2025-12-07T15:46:27Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106445 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T15:46:27Z |
| publishDate | 2007 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| 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 |
| spellingShingle | Dominated Convergence and Egorov Theorems for Filter Convergen Kadets, V. Leonov, A. |
| title | 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_short | Dominated Convergence and Egorov Theorems for Filter Convergen |
| title_sort | dominated convergence and egorov theorems for filter convergen |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106445 |
| work_keys_str_mv | AT kadetsv dominatedconvergenceandegorovtheoremsforfilterconvergen AT leonova dominatedconvergenceandegorovtheoremsforfilterconvergen |