Independence and Alpern multitowers
Let T be any invertible, ergodic, aperiodic measure-preserving transformation of a Lebesgue probability space (X,B,µ), and P any finite measurable partition of X. We show that a (finite) Alpern multitower may always be constructed whose base is independent of P.
Campbell, J., McCutcheon, R., & Windsor, A. (2019). Independence and Alpern multitowers. Dynamical Systems, 34 (2), 239-243. https://doi.org/10.1080/14689367.2018.1504891