Symmetric Birkhoff sums in infinite ergodic theory

Jon Aaronson, Zemer Kosloff, Benjamin Weiss

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We show that the absolutely normalized, symmetric Birkhoff sums of positive integrable functions in infinite, ergodic systems never converge pointwise even though they may be almost surely bounded away from zero and infinity. Also, we consider the latter phenomenon and characterize it among transformations admitting generalized recurrent events.

Original languageAmerican English
Pages (from-to)2394-2416
Number of pages23
JournalErgodic Theory and Dynamical Systems
Issue number8
StatePublished - 1 Dec 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© Cambridge University Press, 2016.


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