Ergodic Theory and Dynamical Systems

Rigidity of the measurable structure for algebraic actions of higher-rank Abelian groups

a1 The University of South Alabama, Mobile, AL 36688, USA (e-mail:
a2 The University of Michigan, Ann Arbor, MI 48109, USA (e-mail:

Article author query
kalinin b   [Google Scholar] 
spatzier r   [Google Scholar] 


We investigate rigidity of measurable structure for higher-rank Abelian algebraic actions. In particular, we show that ergodic measures for these actions fiber over a zero entropy measure with Haar measures along the leaves. We deduce various rigidity theorems for isomorphisms and joinings as corollaries.

(Received July 7 2002)
(Revised October 11 2002)