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An Alpern tower independent of a given partition

James T. Campbell;  Jared T. Collins;  Steven Kalikow;  Raena King;  Randall McCutcheon — 2015

Colloquium Mathematicae

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.

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