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A Multivalued Strong Law of Large Numbers

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  • Pedro Terán

    (Universidad de Oviedo)

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.

Suggested Citation

  • Pedro Terán, 2016. "A Multivalued Strong Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 29(2), pages 349-358, June.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:2:d:10.1007_s10959-014-0572-x
    DOI: 10.1007/s10959-014-0572-x
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    References listed on IDEAS

    as
    1. Zvi Artstein & Sergiu Hart, 1981. "Law of Large Numbers for Random Sets and Allocation Processes," Mathematics of Operations Research, INFORMS, vol. 6(4), pages 485-492, November.
    2. Hess, Christian, 1991. "On multivalued martingales whose values may be unbounded: martingale selectors and mosco convergence," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 175-201, October.
    3. Jérôme Couvreux & Christian Hess, 1999. "A Lévy Type Martingale Convergence Theorem for Random Sets with Unbounded Values," Journal of Theoretical Probability, Springer, vol. 12(4), pages 933-969, October.
    4. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    5. Pedro Terán & Ilya Molchanov, 2006. "The Law of Large Numbers in a Metric Space with a Convex Combination Operation," Journal of Theoretical Probability, Springer, vol. 19(4), pages 875-898, December.
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