On Uniform Laws of Large Numbers for Smoothed Empirical Measures

  • Peter Gaenssler
  • Daniel Rost
Conference paper
Part of the Progress in Probability book series (PRPR, volume 47)


We consider function-indexed smoothed empirical measures on linear metric spaces and focus on uniform laws of large numbers (ULLN) comparable with Glivenko-Cantelli results in the non-smoothed case. Using the random measure process approach we are able to give a set of sufficient conditions for a ULLN which are different from the ones known in the literature and are more close to being necessary.


Weak Convergence Empirical Measure Empirical Process Nonparametric Maximum Likelihood Surable Envelope 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Peter Gaenssler
    • 1
  • Daniel Rost
    • 1
  1. 1.Mathematical InstituteUniversity of MunichMunichGermany

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