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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: 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$.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1992 American Mathematical Society

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