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A Multivalued Strong Law of Large Numbers

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Abstract

We prove a strong law of large numbers for random closed sets in a separable Banach space. It improves upon and unifies the laws of large numbers with convergence in the Wijsman, Mosco and slice topologies, without requiring extra assumptions on either the properties of the space or the kind of sets that can be taken on by the random set as values.

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Acknowledgments

Research partially funded by Spain’s Ministerio de Ciencia e Innovación (TIN2008-06796-C04-04, MTM2011-22993, ECO1022-24181).

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  1. Departamento de Estadística e I.O. y D.M., Escuela Politécnica de Ingeniería, Universidad de Oviedo, 33071, Gijón, Spain

    Pedro Terán

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  1. Pedro Terán
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Correspondence to Pedro Terán.

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Terán, P. A Multivalued Strong Law of Large Numbers. J Theor Probab 29, 349–358 (2016). https://doi.org/10.1007/s10959-014-0572-x

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  • DOI: https://doi.org/10.1007/s10959-014-0572-x

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