Divergence of averages obtained by sampling a flow

Authors:
Mustafa Akcoglu, Alexandra Bellow, Andrés del Junco and Roger L. Jones

Journal:
Proc. Amer. Math. Soc. **118** (1993), 499-505

MSC:
Primary 28D10; Secondary 47A35, 58F11

MathSciNet review:
1143221

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Abstract: In this paper we consider ergodic averages obtained by sampling at discrete times along a measure preserving ergodic flow. We show, in particular, that if is an aperiodic flow, then averages obtained by sampling at times satisfy the strong sweeping out property for any sequence . We also show that there is a flow (which is periodic) and a sequence such that the Cesaro averages of samples at time do converge a.e. In fact, we show that every uniformly distributed sequence admits a perturbation that makes it a good Lebesgue sequence.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1143221-1

Keywords:
Ergodic flow,
good Lebesgue sequences,
uniform distribution

Article copyright:
© Copyright 1993
American Mathematical Society