New York Journal of Mathematics
Volume 3A (1997-1998) 11-14


S. J. Eigen and V. S. Prasad

Multiple Rokhlin Tower Theorem: A Simple Proof

Published: November 24, 1997
Keywords: Rokhlin Tower
Subject: Primary 28D05; Secondary 58F11

S. Alpern has proved that an invertible antiperiodic measurable measure preserving transformation of a Lebesgue probability space can be represented by k towers of heights n1, ..., nk, with prescribed measures, provided that the heights have greatest common divisor 1. In this paper we give a simple proof of Alpern's theorem. It is elementary in the sense that it involves no limits and uses Kakutani's easy proof of Rokhlin's Lemma.

Author information

S. J. Eigen:
Northeastern University, Boston MA 02115

V. S. Prasad:
University of Massachusetts, Lowell MA 01854