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Glivenko-Cantelli type theorems: An application of the convergence theory of stochastic suprema

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Abstract

The uniform convergence of empirical processes on certain classes of sets follows from the convergence theory for random lower semicontinuous functions studies in the context of stochastic optimization. In the process, a richer class of sets for which one can prove this type of result is exhibited.

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Authors and Affiliations

  1. Università “La Sapienza”, 00100, Roma, Italy

    Gabriella Salinetti

  2. University of California, 95616, Davis, CA, USA

    Roger J. -B. Wets

Authors
  1. Gabriella Salinetti
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  2. Roger J. -B. Wets
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Research supported in part by grants from Ministero Publica Istruzione and the National Science Foundation.

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Salinetti, G., Wets, R.J.B. Glivenko-Cantelli type theorems: An application of the convergence theory of stochastic suprema. Ann Oper Res 30, 157–168 (1991). https://doi.org/10.1007/BF02204814

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