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A uniform strong law of large numbers for partial sum processes of Banach space-valued random sets

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  • Jang, Lee-Chae
  • Kwon, Joong-Sung

Abstract

We consider random sets as (measurable) mappings from a probability space into the set of compact convex subsets of a Banach space and prove a uniform strong law of large numbers for sequences of independent and identically distributed random sets. Our results generalize those of Bass and Pyke (1984).

Suggested Citation

  • Jang, Lee-Chae & Kwon, Joong-Sung, 1998. "A uniform strong law of large numbers for partial sum processes of Banach space-valued random sets," Statistics & Probability Letters, Elsevier, vol. 38(1), pages 21-25, May.
    • Handle: RePEc:eee:stapro:v:38:y:1998:i:1:p:21-25
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    References listed on IDEAS

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    1. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
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