New York Journal of Mathematics
Volume 10 (2004) 249-269


David Fisher, Dave Witte Morris, and Kevin Whyte

Nonergodic actions, cocycles and superrigidity

Published: August 31, 2004
Keywords: Borel action, nonergodic, ergodic component, Borel cocycle, superrigidity, von Neumann Selection Theorem
Subject: 28D15

This paper proves various results concerning nonergodic actions of locally compact groups and particularly Borel cocycles defined over such actions. The general philosophy is to reduce the study of the cocycle to the study of its restriction to each ergodic component of the action, while being careful to show that all objects arising in the analysis depend measurably on the ergodic component. This allows us to prove a version of the superrigidity theorems for cocycles defined over nonergodic actions.


This research was partially supported by the National Science Foundation (grants DMS-0226121, DMS-0100438, and DMS-0204576). The first author was also partially supported by a PSC-CUNY grant.

Author information

David Fisher:
Department of Mathematics and Computer Science, Lehman College - CUNY, 250 Bedford Park Boulevard W., Bronx, NY 10468

Dave Witte Morris:
Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, AB, T1K 3M4, Canada

Kevin Whyte:
Department of Mathematics, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607-7045