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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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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
PII: S 0002-9947(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.