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Divergence of Averages Obtained by Sampling a Flow

Mustafa Akcoglu, Alexandra Bellow, Andres del Junco and Roger L. Jones
Proceedings of the American Mathematical Society
Vol. 118, No. 2 (Jun., 1993), pp. 499-505
DOI: 10.2307/2160329
Stable URL: http://www.jstor.org/stable/2160329
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Divergence of Averages Obtained by Sampling a Flow
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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 Ut is an aperiodic flow, then averages obtained by sampling at times n + tn satisfy the strong sweeping out property for any sequence tn → 0. We also show that there is a flow (which is periodic) and a sequence tn → 0 such that the Cesaro averages of samples at time n + tn 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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