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

A note on an ergodic theorem in weakly uniformly convex geodesic spaces