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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Second order ergodic theorems for ergodic transformations of infinite measure spaces
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by Jon Aaronson, Manfred Denker and Albert M. Fisher PDF
Proc. Amer. Math. Soc. 114 (1992), 115-127 Request permission

Abstract:

For certain pointwise dual ergodic transformations $T$ we prove almost sure convergence of the log-averages \[ \frac {1}{{\log N}}\sum \limits _{n = 1}^N {\frac {1}{{na\left ( n \right )}}\sum \limits _{k = 1}^n {f \circ {T^k}\left ( {f \in {L_1}} \right )} } \] and the Chung-Erdös averages \[ \frac {1}{{\log a\left ( N \right )}}\sum \limits _{k = 1}^N {\frac {1}{{a\left ( k \right )}}f \circ {T^k}} \left ( {f \in L_1^ + } \right )\] towards $\smallint f$, where $a\left ( n \right )$ denotes the return sequence of $T$.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 114 (1992), 115-127
  • MSC: Primary 28D05; Secondary 60F15
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1099339-4
  • MathSciNet review: 1099339