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Let $ \Gamma < PSL_2(\mathbb{C}) $ be a Zariski dense finitely generatedKleinian group. We show all Radon measures on $ PSL_2(\mathbb{C}) / \Gamma $which are ergodic and invariant under the action of the horospherical subgroupare either supported on a single closed horospherical orbit or quasi-invariantwith respect to the geodesic frame flow and its centralizer. We do this byapplying a result of Landesberg and Lindenstrauss together with fundamentalresults in the theory of 3-manifolds, most notably the Tameness Theorem by Agoland Calegari-Gabai.

Horospherically invariant measures and finitely generated Kleinian groups