On the Mori-Szekely conjectures for the Borel-Cantelli lemma
Chunrong Feng, Liangpan Li
TL;DR
This paper constructs counterexamples to disprove two conjectures related to the Borel-Cantelli lemma, clarifying the limitations of these conjectures in probability theory.
Contribution
It provides the first known counterexamples that disprove the Mori-Szekely conjectures for the Borel-Cantelli lemma.
Findings
Counterexamples show the conjectures are false
Clarifies the boundaries of the Borel-Cantelli lemma
Refutes previous assumptions about the conjectures
Abstract
The purpose of this note is to show by constructing counterexamples that two conjectures of M\'{o}ri and Sz\'{e}kely for the Borel-Cantelli lemma are false.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Algebra and Geometry · Analytic Number Theory Research