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On a uniform law of large numbers for random sets and subdifferentials of random functions

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  • Terán, Pedro

Abstract

In this paper, we strengthen the convergence in a uniform law of large numbers for random upper semicontinuous multifunctions of Shapiro and Xu. The proof is based on an abstract law of large numbers in a metric space endowed with a convex combination operation. Convergence in the Hausdorff metric is obtained, whereas the original result presented a weakened form of convergence of excess functionals. As a consequence, another law of large numbers for subdifferentials of random functions is improved as well.

Suggested Citation

  • Terán, Pedro, 2008. "On a uniform law of large numbers for random sets and subdifferentials of random functions," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 42-49, January.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:1:p:42-49
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    References listed on IDEAS

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    1. Etemadi, N. & Kaminski, M., 1996. "Strong law of large numbers for 2-exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 245-250, July.
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