  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
amenability and ergodicity properties, we prove the existence of equivariant
maps from $B$ to the visual boundary $\partial X$.
