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Decomposition and factorization of measures

  • Ole E. Barndorff-Nielsen
  • Preben Blæsild
  • Poul Svante Eriksen
Part of the Lecture Notes in Statistics book series (LNS, volume 58)

Abstract

Suppose a space χ is partitioned into disjoint subsets χπ,π∈ П, and let μ be a measure on χ. If for each π∈ П we have a measure ρπ on χπ and if there is a measure κ on П such that \(\mathop \smallint \limits_X f\left( x \right)d\mu \left( x \right) = \mathop \smallint \limits_\Pi \mathop \smallint \limits_{{x_\pi }} f\left( x \right)d{\rho _\pi }\left( x \right)d\kappa \left( \pi \right)\) for every integrable function f then ((ρπ)π∈П,κ) is said to constitute a decomposition of μ, and we speak of (5.1) as a disintegration formula.

Keywords

Riemannian Manifold Normal Subgroup Invariant Measure Orbit Space Geometric Measure 
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-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Ole E. Barndorff-Nielsen
    • 1
  • Preben Blæsild
    • 1
  • Poul Svante Eriksen
    • 2
  1. 1.Department of Theoretical Statistics Institute of MathematicsAarhus UniversityAarhusDenmark
  2. 2.Department of Mathematics and Computer Science Institute of Electronic SystemsAalborg University CenterAalborgDenmark

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