Ergodic Theory and Dynamical Systems

We consider actions of locally compact groups G on certain CAT(0) spaces X by isometries. The CAT(0) spaces we consider have finite dimension at large scale. In case B is a G-boundary, that is a measurable G-space with some amenability and ergodicity properties, we prove the existence of equivariant maps from B to the visual boundary ∂X .

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