Ergodic Theory and Dynamical Systems

Research Article

Epimorphic subgroups and invariant measures

Shahar Mozesa1

a1 Department of Mathematics, Hebrew University, Jerusalem 91904 Israel

Abstract

It is shown that a probability measure on a homogeneous space Γ\G which is invariant under a subgroup H < G which is epimorphic in a subgroup L < G is invariant under L. When L = G we obtain a subgroup H such that for any lattice Γ < G its action on Γ\G is uniquely ergodic.

(Received December 23 1993)