ABSTRACT Let T be any invertible, ergodic, aperiodic measure-preserving transformation of a Lebesgue probability space , 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.

中文翻译：

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Independence 和 Alpern Multitowers

摘要 设 T 是 Lebesgue 概率空间 的任何可逆的、遍历的、非周期的保测变换，P 是 X 的任何有限可测分区。我们表明，总是可以构建一个（有限）Alpern 多塔，其基础独立于 P。