STABILIZERS FOR ERGODIC ACTIONS OF HIGHER RANK SEMISIMPLE GROUPS

Let G be a connected semisimple Lie group with finite center and R-ran k greater-than-or-equal-to 2. Suppose that each simple factor of G eit her has R-rank greater-than-or-equal-to 2 or is locally isomorphic to Sp(1,n) or F4(-20). We prove that any faithful, in-educible, properly ergodic, finite measure-preserving action of G is essentially free. We extend the result to reducible actions and actions of lattices.