Published online by Cambridge University Press: 13 April 2015
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
$\partial X$.