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

Published online by Cambridge University Press:  22 December 2004

BORIS KALININ  and
RALF SPATZIER
BORIS KALININ
Affiliation:
The University of South Alabama, Mobile, AL 36688, USA (e-mail: kalinin@jaguar1.usouthal.edu)
RALF SPATZIER
Affiliation:
The University of Michigan, Ann Arbor, MI 48109, USA (e-mail: spatzier@umich.edu)
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 1 , February 2005 , pp. 175 - 200
Copyright
2004 Cambridge University Press

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