F. Alcalde Cuesta. Moyennes harmoniques. Annales de la Faculté des Sciences de Toulouse, XIX (2010), 493-512.

Abstract. We introduce a notion of stationary mean for random walks on graphed measured equivalence relations, which generalizes the classical notion of invariant mean. For graphings of bounded geometry, such mean always exists. We prove that any stationary mean becomes invariant if the random walk on a.e. orbit has good asymptotic properties such as triviality of Poisson boundary or recurrence.