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Convergence of Averages in Ergodic Theory
Butkevich, Sergey G

2001, Doctor of Philosophy, Ohio State University, Mathematics.
Von Neumann's Mean Ergodic Theorem and Birkhoff's Pointwise Ergodic Theorem lie in the foundation of Ergodic Theory. Over the years there have been many generalizations of the two, most recently a version of pointwise ergodic theorem for measure-preserving actions of amenable groups due to Elon Lindenstrauss. In the first chapter, we extend some of Lindenstrauss' results to measure-preserving actions of countable left-cancellative amenable semigroups and to averaging along more general types of Folner sequences.

In the next three chapters, we study convergence of Cesaro averages of a special form for measure-preserving actions of countable amenable groups. We extend some of the results obtained by D.Berend and V.Bergelson for joint properties of Z-actions to joint properties of actions of countable amenable groups. In particular, we obtain a criterion for joint ergodicity of actions of countable amenable groups by automorphisms of a not necessarily abelian compact group.

In the last chapter of this dissertation, we investigate convergence of Cesaro averages for two non-commuting measure-preserving transformations along a regular sequence of intervals.

Vitaly Bergelson (Advisor)

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Butkevich, S. (2001). Convergence of Averages in Ergodic Theory. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Butkevich, Sergey. "Convergence of Averages in Ergodic Theory." Electronic Thesis or Dissertation. Ohio State University, 2001. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Butkevich, Sergey "Convergence of Averages in Ergodic Theory." Electronic Thesis or Dissertation. Ohio State University, 2001. https://etd.ohiolink.edu/

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