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An Alpern tower independent of a given partition

Volume 141 / 2015

James T. Campbell, Jared T. Collins, Steven Kalikow, Raena King, Randall McCutcheon Colloquium Mathematicum 141 (2015), 119-124 MSC: Primary 28D05; Secondary 37M25, 60A10. DOI: 10.4064/cm141-1-10

Abstract

Given a measure-preserving transformation $T$ of a probability space $(X, \mathcal B, \mu )$ and a finite measurable partition $\mathbb P$ of $X$, we show how to construct an Alpern tower of any height whose base is independent of the partition $\mathbb P$. That is, given $N \in {\mathbb N} $, there exists a Rokhlin tower of height $N$, with base $B$ and error set $E$, such that $B$ is independent of $\mathbb P$, and $TE \subset B$.

Authors

  • James T. CampbellDepartment of Mathematical Sciences
    University of Memphis
    Dunn Hall 373
    Memphis, TN 38152, U.S.A.
    e-mail
  • Jared T. CollinsDepartment of Mathematics
    and Computer Science
    Freed-Hardeman University
    Henderson, TN 38340, U.S.A.
    e-mail
  • Steven KalikowDepartment of Mathematical Sciences
    University of Memphis
    Dunn Hall 373
    Memphis, TN 38152, U.S.A.
    e-mail
  • Raena KingDepartment of Mathematics
    and Computer Science
    Christian Brothers University
    Memphis, TN 38104, U.S.A.
    e-mail
  • Randall McCutcheonDepartment of Mathematical Sciences
    University of Memphis
    Dunn Hall 373
    Memphis, TN 38152, U.S.A.
    e-mail

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