Dominated Convergence and Egorov Theorems for Filter Convergence

Автор(и)

  • V. Kadets Department of Mechanics and Mathematics, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61077, Ukraine
  • A. Leonov Department of Mechanics and Mathematics, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61077, Ukraine

Анотація

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.

Mathematics Subject Classification: 28A20, 54A20, 40C05.

Ключові слова:

measure theory, dominated convergence theorem, Egorov theorem, filter convergence, statistical convergence, matrix summability.

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Як цитувати

(1)
Kadets, V.; Leonov, A. Dominated Convergence and Egorov Theorems for Filter Convergence . Журн. мат. фіз. анал. геом. 2007, 3, 196-212.

Номер

Том 3 № 2 (2007)

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