@article{Kadets_Leonov_2007, place={Харків, Україна}, title={Dominated Convergence and Egorov Theorems for Filter Convergen}, volume={3}, url={https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/jm03-0196e}, abstractNote={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.}, number={2}, journal={Журнал математичної фізики, аналізу, геометрії}, author={Kadets, V. and Leonov, A.}, year={2007}, month={Трав}, pages={196–212} }