Abstract
We prove extension of classical convergence theorem of P. Lévy for martingales of random subsets of a metric space of negative curvature.
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Herer, W.: Espérance mathématique d'une variable aléatoire à courbure négative, C.R. Acad. Sci. Paris Sér. I 306 (1988), 681–684.
Herer, W.: Martingales à valeurs fermées bornées d'un espace métrique à courbure négative, C.R. Acad. Sci. Paris Sér. I 307 (1988), 997–1000.
Herer, W.: Mathematical expectation and strong law of large numbers for random variables with values in a metric space of negative curvature, Prob. Math. Statist. 13(1) (1992), 59–70.
Himmelberg, C. J.: Measurable relations, Fund. Math. 87 (1975), 53–72.
Matheron, G.: Random Sets and Integral Geometry, Wiley, New York, 1975.
Neveu, J.: Bases mathématiques du calcul des probabilités, Masson, Paris, 1964.
Partasarathy, K. R.: Introduction to Probability and Measure, Springer-Verlag, New York, 1978.
Ricceri, B.: Sur l'approximation de sélections mesurables, C.R. Acad. Sci. Paris Sér. I 295 (1983), 527–530.
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Herer, W. Martingales of Random Subsets of a Metric Space of Negative Curvature. Set-Valued Analysis 5, 147–157 (1997). https://doi.org/10.1023/A:1008630912958
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DOI: https://doi.org/10.1023/A:1008630912958