Universal Donsker Classes and Type 2

  • Joel Zinn
Part of the Progress in Probability book series (PRPR, volume 20)


In this note we give a partial analogue of a theorem of Pisier [6], which relates the universal Donsker property for classes of sets to a type 2 condition. Actually what we give here is less delicate, since it does not require the useful Lemma 7.13 of Dudley [1]. We start with some


Banach Space Central Limit Theorem Gaussian Process Measurable Space Radon Measure 
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  1. [1]
    R.M. Dudley, Central limit theorems for empirical measures, Ann. Probab. 6 (1978), 899–929.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    A course on empirical processes,pp. 1–142 in “École d’Été de Probabilités de Saint-Flour XII-1982”, Lecture Notes in Math. 1097. Springer Verlag 1984.Google Scholar
  3. [3]
    Universal Donaker classes and metric entropy. Preprint.Google Scholar
  4. [4]
    M Durst and R.M. Dudley, Empirical processes, Vapnik-Oeroonenkis classes and Poisson processes, Probab. Math. Statist. 1 (1981), 109–115.MathSciNetGoogle Scholar
  5. [5]
    E. Giné and J. Zinn, Some limit theorems for empirical processes, Ann. Probab. 12 (1984), 929–989.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    G. Pisier, Remarques sur les classes de Vapnik-Öervonenkis, Ann. Inst. H. Poincaré 20 (1984), 287–298.MathSciNetMATHGoogle Scholar

Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • Joel Zinn
    • 1
  1. 1.Department of MathematicsTexas A & M UniversityCollege StationUSA

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