Minimality and unique ergodicity for subgroup actions

Let G be an B-algebraic semisimple group, H an algebraic R-subgroup. and Ga mma a lattice in G. Partially answering a question posed by Hillel Furstenb erg in 1972, we prove that if the action of H on G/Gamma is minimal, then i t is uniquely ergodic. Our proof uses in an essential way Marina Ratner's c lassification of probability measures on G/Gamma invariant under unipotent elements, and the study of "tubes" in G/Gamma.