An alpern tower independent of a given partition


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.

Publication Title

Colloquium Mathematicum