On L¹ convergence of barycentric sequences of empirical measures

Abstract

In a previous article we proved a pointwise ergodic theorem for or sequences of barycentres of empirical measures which are defined from the action of Fuchsian groups and for L 2 maps valuated in CAT(0) spaces. In this note we extend this result to the L 1 -setting for maps valuated in nonpositively curved spaces.