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Pure Mathematics

From discrete- to continuous-time ergodic theorems

Profile image of Alexander LeibmanAlexander Leibman

2012, Ergodic Theory and Dynamical Systems

https://doi.org/10.1017/S0143385711000848
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Abstract

We introduce methods that allow us to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results of interest.

Figures (7)
+ Here and below, T’f(w) = f(T’), t €R, w € X, and the integral pe T'f dt is understood in the sense of Bochner.
+ Here and below, T’f(w) = f(T’), t €R, w € X, and the integral pe T'f dt is understood in the sense of Bochner.
and, as in the proof of Theorem 4.5, by Fatou’s lemma,
and, as in the proof of Theorem 4.5, by Fatou’s lemma,

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References (27)

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