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Symmetric Birkhoff sums in infinite ergodic theory
Published online by Cambridge University Press: 04 July 2016
Abstract
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.
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- © Cambridge University Press, 2016
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