  Karlsson and Margulis proved in the setting of uniformly convex geodesic
spaces, which additionally satisfy a nonpositive curvature condition, an
ergodic theorem that focuses on the asymptotic behavior of integrable cocycles
of nonexpansive mappings over an ergodic measure-preserving transformation. In
this note we show that this result holds true when assuming a weaker notion of
uniform convexity.
