Contiguity

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

Abstract

Let P and Q be probability measures on a measurable space (Ω, A). If Q is absolutely continuous with respect to P, then the Q-law of a measurable map X: Ω ↦ D can be calculated from the P-law of the pair (X, dQ/dP) through the formula
$${E_Q}f(X) = {E_P}f(X)\frac{{dQ}}{{dP}}$$

Keywords

Probability Measure Measurable Space Random Element Empirical Process Continuous Mapping Theorem 
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.

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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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