A Borel-Cantelli lemma and its applications

Abstract

We give a version of the Borel-Cantelli lemma. As an application, we prove an almost sure local central limit theorem. As another application, we prove a dynamical Borel-Cantelli lemma for systems with sufficiently fast decay of correlations with respect to Lipschitz observables.

References in corpus (2)

• A sharp correlation inequality with an application to almost sure local limit theorem
• Ergodic properties of Viana-like maps with singularities in the base dynamics