Open AccessOn a strong form of the Borel-Cantelli lemma
Author(s) -
Alexander O. Frolov
Publication year - 2022
Publication title -
vestnik sankt-peterburgskogo universiteta. matematika. mehanika. astronomiâ/vestnik sankt-peterburgskogo universiteta. seriâ 1, matematika, mehanika, astronomiâ
Language(s) - English
Resource type - Journals
eISSN - 2587-5884
pISSN - 1025-3106
DOI - 10.21638/spbu01.2022.109
Subject(s) - lemma (botany) , mathematics , function (biology) , combinatorics , pure mathematics , discrete mathematics , ecology , poaceae , evolutionary biology , biology
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.