A Borel-Cantelli lemma and its applications

Author:
Nuno Luzia

Journal:
Trans. Amer. Math. Soc. **366** (2014), 547-560

MSC (2010):
Primary 60F05; Secondary 37A30

Published electronically:
July 1, 2013

MathSciNet review:
3118406

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

**Nuno Luzia**

Affiliation:
Universidade Federal do Rio de Janeiro, Instituto de Matemática, Rio de Janeiro 21945-970, Brazil

Email:
nuno@im.ufrj.br

DOI:
http://dx.doi.org/10.1090/S0002-9947-2013-06028-X

Keywords:
Borel-Cantelli lemma,
almost sure local central limit theorem,
decay of correlations.

Received by editor(s):
January 31, 2012

Received by editor(s) in revised form:
July 16, 2012

Published electronically:
July 1, 2013

Additional Notes:
The author was partially supported by Fundação para a Ciência e a Tecnologia through the project "Randomness in Deterministic Dynamical Systems and Applications" (PTDC/MAT/105448/2008).

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.