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Proceedings of the American Mathematical Society

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

 

 

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 $ {U_t}$ is an aperiodic flow, then averages obtained by sampling at times $ n + {t_n}$ satisfy the strong sweeping out property for any sequence $ {t_n} \to 0$. We also show that there is a flow (which is periodic) and a sequence $ {t_n} \to 0$ such that the Cesaro averages of samples at time $ n + {t_n}$ 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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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