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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Second order ergodic theorems for ergodic transformations of infinite measure spaces


Authors: Jon Aaronson, Manfred Denker and Albert M. Fisher
Journal: Proc. Amer. Math. Soc. 114 (1992), 115-127
MSC: Primary 28D05; Secondary 60F15
MathSciNet review: 1099339
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Abstract | References | Similar Articles | Additional Information

Abstract: For certain pointwise dual ergodic transformations $ T$ we prove almost sure convergence of the log-averages

$\displaystyle \frac{1}{{\log N}}\sum\limits_{n = 1}^N {\frac{1}{{na\left( n \right)}}\sum\limits_{k = 1}^n {f \circ {T^k}\left( {f \in {L_1}} \right)} } $

and the Chung-Erdös averages

$\displaystyle \frac{1}{{\log a\left( N \right)}}\sum\limits_{k = 1}^N {\frac{1}{{a\left( k \right)}}f \circ {T^k}} \left( {f \in L_1^ + } \right)$

towards $ \smallint f$, where $ a\left( n \right)$ denotes the return sequence of $ T$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1099339-4
PII: S 0002-9939(1992)1099339-4
Article copyright: © Copyright 1992 American Mathematical Society



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