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


The continuous mapping theorems for the three modes of stochastic convergence considered so far can be refined to cover maps g n (X n ), rather than g(X n ), for a fixed g. Then the g n should have a property that might be called asymptotic equicontinuity almost everywhere under the limit measure.


Representation Theorem Continuity Property Dominate Convergence Theorem Limit Measure Empirical Process 


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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

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