  Let G=PSL(2, F) where F= R or C, and consider the space Z=(\Gamma_1 x
\Gamma_2)\ (G x G) where \Gamma_1<G is a co-compact lattice and \Gamma_2<G is a
finitely generated discrete Zariski dense subgroup. The work of Benoist-Quint
gives a classification of all ergodic invariant Radon measures on Z for the
diagonal G-action. In this paper, for a horospherical subgroup N of G, we
classify all ergodic, conservative, invariant Radon measures on Z for the
diagonal N-action, under the additional assumption that \Gamma_2 is
geometrically finite.
