Geodesic
An Alpern tower independent of a given partition
James T. Campbell 1   ; Jared T. Collins 2   ; Steven Kalikow 1   ; Raena King 3   ; Randall McCutcheon 1
1 Department of Mathematical Sciences University of Memphis Dunn Hall 373 Memphis, TN 38152, U.S.A.
2 Department of Mathematics and Computer Science Freed-Hardeman University Henderson, TN 38340, U.S.A.
3 Department of Mathematics and Computer Science Christian Brothers University Memphis, TN 38104, U.S.A.
Colloquium Mathematicum, Tome 141 (2015) no. 1, pp. 119-124 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $TE \subset B$.
DOI : 10.4064/cm141-1-10
Keywords: given measure preserving transformation probability space nbsp mathcal finite measurable partition mathbb construct alpern tower height whose base independent partition nbsp mathbb given mathbb there exists rokhlin tower height base error set nbsp independent nbsp mathbb subset

James T. Campbell  1   ; Jared T. Collins  2   ; Steven Kalikow  1   ; Raena King  3   ; Randall McCutcheon  1

1 Department of Mathematical Sciences University of Memphis Dunn Hall 373 Memphis, TN 38152, U.S.A.
2 Department of Mathematics and Computer Science Freed-Hardeman University Henderson, TN 38340, U.S.A.
3 Department of Mathematics and Computer Science Christian Brothers University Memphis, TN 38104, U.S.A. 
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James T. Campbell; Jared T. Collins; Steven Kalikow; Raena King; Randall McCutcheon. An Alpern tower independent of a given partition. Colloquium Mathematicum, Tome 141 (2015) no. 1, pp. 119-124. doi: 10.4064/cm141-1-10

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