Stabilizers for Ergodic Actions of Higher Rank Semisimple Groups

Let G be a connected semisimple Lie group with finite center and R-rank > 2. Suppose that each simple factor of G either has R-rank > 2 or is locally isomorphic to Sp(l, n) or F4(-20). We prove that any faithful, irreducible, properly ergodic, finite measure-preserving action of G is essentially free. We extend the result to reducible actions and actions of lattices.