Given a measure-preserving transformation T of a probability space (X,ℬ,μ) and a finite measurable partition ℙ of X, we show how to construct an Alpern tower of any height whose base is independent of the partition ℙ. That is, given N ∈ ℕ, there exists a Rokhlin tower of height N, with base B and error set E, such that B is independent of ℙ, and TE ⊂ B.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-1-10,
author = {James T. Campbell and Jared T. Collins and Steven Kalikow and Raena King and Randall McCutcheon},
title = {An Alpern tower independent of a given partition},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {119-124},
zbl = {1323.28019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-1-10}
}
James T. Campbell; Jared T. Collins; Steven Kalikow; Raena King; Randall McCutcheon. An Alpern tower independent of a given partition. Colloquium Mathematicae, Tome 139 (2015) pp. 119-124. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-1-10/