A Borel-Cantelli lemma and its applications
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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.References
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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
- 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).
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 547-560
- MSC (2010): Primary 60F05; Secondary 37A30
- DOI: https://doi.org/10.1090/S0002-9947-2013-06028-X
- MathSciNet review: 3118406