  We prove that a non-elementary measurable cocycle in the isometry group of a
CAT(0)-space of finite telescopic dimension admits a Furstenberg map. We also
show that a maximal cocycle $\sigma:\Gamma \times X \rightarrow
\text{PU}(p,\infty)$ where $\Gamma < \text{PU}(n,1)$ is a torsion-free lattice
and $(X,\mu_X)$ is a ergodic standard Borel $\Gamma$-space is finitely
reducible. As a consequence, we prove an infinite dimensional rigidity
phenomenon for cocycles.
