Divergence of averages obtained by sampling a flow
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- by Mustafa Akcoglu, Alexandra Bellow, Andrés del Junco and Roger L. Jones PDF
- Proc. Amer. Math. Soc. 118 (1993), 499-505 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 499-505
- MSC: Primary 28D10; Secondary 47A35, 58F11
- DOI: https://doi.org/10.1090/S0002-9939-1993-1143221-1
- MathSciNet review: 1143221