MEASURABLE QUOTIENTS OF UNIPOTENT TRANSLATIONS ON HOMOGENEOUS SPACES

Let U be a nilpotent, unipotent subgroup of a Lie group G, and let GAM MA be a closed subgroup of G. Marina Ratner showed that every ergodic U-invariant probability measure on the homogeneous space GAMMA\G is of a simple algebraic form. We use this fundamental new result to show t hat every measureable quotient of the U-action of GAMMA\G is of a simp le algebraic form. Roughly speaking, any quotient is a double-coset sp ace LAMBDA\G/K.