title: On a strong form of the Borel - Cantelli lemma
metadata.name: dc.contributor.author
metadata.value: Frolov, Andrei N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-04-14T11:32:15Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-04-14T11:32:15Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Frolov А.N. On a strong form of the Borel - Cantelli lemma. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 1, pp. 85–93.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.109
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/36157
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The strong form of the Borel Cantelli lemma is a variant of the strong law of large numbers
  for sums of the indicators of events. These sums are centered at the mean and normalized
  by some function from sums of probabilities of events. The series from probabilities is assumed
  to be divergent. In this paper, we derive new strong forms of the Borel - Cantelli
  lemma with smaller normalizing sequences than it was before. Conditions on variations
  of increments of indicators become stronger. We give examples in which these conditions
  hold.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 9; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: the Borel-Cantelli lemma
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the quantitative Borel-Cantelli lemma
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: strong forms of the Borel-Cantelli lemma
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: suns of indicators of events
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: strong law of large numbers
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: almost surely convergence
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On a strong form of the Borel - Cantelli lemma
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 85-93.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/36157/1/85-93.pdf
resources.format: Adobe PDF
resources.size: 297,46 kB