An Alpern tower independent of a given partition
James T. Campbell, Jared T. Collins, Steven Kalikow, Raena King, Randall McCutcheon (2015)
Colloquium Mathematicae
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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.