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dc.contributor.author | Al Hayek N. | |
dc.contributor.author | Ordóñez Cabrera M. | |
dc.contributor.author | Rosalsky A. | |
dc.contributor.author | Ünver M. | |
dc.contributor.author | Volodin A. | |
dc.date.accessioned | 2022-02-09T20:30:46Z | |
dc.date.available | 2022-02-09T20:30:46Z | |
dc.date.issued | 2021 | |
dc.identifier.issn | 0010-0757 | |
dc.identifier.uri | https://dspace.kpfu.ru/xmlui/handle/net/168660 | |
dc.description.abstract | In this article, the concept of J-uniform integrability of a sequence of random variables { Xk} with respect to { ank} is introduced where J is a non-trivial ideal of subsets of the set of positive integers and { ank} is an array of real numbers. We show that this concept is weaker than the concept of { Xk} being uniformly integrable with respect to { ank} and is more general than the concept of B-statistical uniform integrability with respect to { ank}. We give two characterizations of J-uniform integrability with respect to { ank}. One of them is a de La Vallée Poussin type characterization. For a sequence of pairwise independent random variables { Xk} which is J-uniformly integrable with respect to { ank} , a law of large numbers with mean ideal convergence is proved. We also obtain a version without the pairwise independence assumption by strengthening other conditions. Supplements to the classical Mean Convergence Criterion are also established. | |
dc.relation.ispartofseries | Collectanea Mathematica | |
dc.subject | Mean convergence | |
dc.subject | Sequence of random variables | |
dc.subject | Summability methods | |
dc.subject | Uniform integrability | |
dc.subject | Weighted sums | |
dc.title | Some results concerning ideal and classical uniform integrability and mean convergence | |
dc.type | Article | |
dc.collection | Публикации сотрудников КФУ | |
dc.source.id | SCOPUS00100757-2021-SID85115091715 |