Dominated Convergence and Egorov Theorems for Filter Convergen
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Dominated Convergence and Egorov Theorems for Filter Convergen
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| Creator |
Kadets, V.
Leonov, A. |
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| 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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| Date |
2016-09-28T19:02:31Z
2016-09-28T19:02:31Z 2007 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/106445 |
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| Language |
en
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| Relation |
Журнал математической физики, анализа, геометрии
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| Publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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