Symmetrization and Measurability

  • Aad W. van der Vaart
  • Jon A. Wellner
Part of the Springer Series in Statistics book series (SSS)


One of the two main approaches toward deriving Glivenko-Cantelli and Donsker theorems is based on the principle of comparing the empirical process to a “symmetrized” empirical process. In this chapter we derive the main symmetrization theorem, as well as a number of technical complements, which may be skipped at first reading.


Outer Probability Empirical Process Coordinate Projection Complete Probability Space Tight Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Aad W. van der Vaart
    • 1
  • Jon A. Wellner
    • 2
  1. 1.Department of Mathematics and Computer ScienceFree UniversityAmsterdamThe Netherlands
  2. 2.StatisticsUniversity of WashingtonSeattleUSA

Personalised recommendations