Rigidity properties of higher rank abelian actions
Abstract. We discuss rigidity of measurable structure for higher rank abelian algebraic actions. In particular, we show that ergodic measures for these actions fiber over a 0 entropy measure with Haar measures along the leaves. We deduce various rigidity theorems for isomorphisms and joinings as corollaries. We also discuss some rigidity properties of nonalgebraic Anosov actions.