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Pointwise ergodic theorem and strong law of large numbers for random points in a metric space with negative curvature. (Théorème ergodique ponctuel et lois fortes des grands nombres pour des points aléatoires d’un espace métrique à courbure négative.) (French) Zbl 0880.60026
Summary: Let \(M\) be a complete separable metric space with negative curvature as defined by Herer. Using Herer’s definition of the mathematical expectation of a random point of \(M\), we extend to sequences of random points of \(M\) a pointwise ergodic theorem and strong laws of large numbers (SLLN), known in the case, where \(M\) is a separable Banach space (SLLN of Etemadi, of Beck and Giesy and of Cuesta and Matrán). The convergence results obtained here are stated for the Hausdorff topology or the Wijsman topology in the space of closed subsets of \(M\).

60F15 Strong limit theorems
60B05 Probability measures on topological spaces
60D05 Geometric probability and stochastic geometry
51K05 General theory of distance geometry
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