Projects per year
Abstract
Let $(\Omega, \mathcal{A}, \mu)$ be a probability space. The classical BorelCantelli Lemma states that for any sequence of $\mu$measurable sets $E_i$ ($i=1,2,3,\dots$), if the sum of their measures converges then the corresponding $\limsup$ set $E_\infty$ is of measure zero. In general the converse statement is false. However, it is well known that the divergence counterpart is true under various additional `independence' hypotheses. In this paper we revisit these hypotheses and establish both sufficient and necessary conditions for $E_\infty$ to have either positive or full measure.
Original language  English 

Article number  126750 
Number of pages  21 
Journal  Journal of mathematical analysis and applications 
Volume  519 
Issue number  1 
Early online date  13 Oct 2022 
DOIs  
Publication status  Published  1 Mar 2023 
Bibliographical note
© 2022 The Author(s).Projects
 1 Finished

Programme GrantNew Frameworks in metric Number Theory
1/06/12 → 30/11/18
Project: Research project (funded) › Research