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

BORIS KALININ, RALF SPATZIER
2005 Ergodic Theory and Dynamical Systems  
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.
doi:10.1017/s014338570400046x fatcat:j7il7upw3nglphdrfi7ku432zu