An Alpern tower independent of a given partition
Volume 141 / 2015
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 $TE \subset B$.
