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

Manifold 

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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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