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We study the outer automorphism group OutRr of the ergodic equivalence relation Rr generated by the action of a lattice F in a semisimple Lie group on the homogeneos space of a compact group K. It is shown that OutRr is locally compact. If K is a connected simple Lie group, we prove the compactness of 0\itR r using the D. Witte's rigidity theorem. Moreover, an example of an equivalence relation without outer automorphisms is constructed.doi:10.2977/prims/1195162855 fatcat:unskl2wzvzehhf3kxabli4jigi