AN ALPERN TOWER INDEPENDENT OF A GIVEN PARTITION

作者：Campbell James T^*; Collins Jared T; Kalikow Steven; King Raena; Mccutcheon Randall

来源：Colloquium Mathematicum, 2015, 141(1): 119-124.

DOI：10.4064/cm141-1-10

• Rokhlin tower
• Alpern tower
• independent sets
• measure-preserving transformation
• probability space

Given a measure-preserving transformation T of a probability space (X, B, mu) 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 is an element of 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 subset of B.

• 出版日期2015