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Invariant measures and disintegrations with applications to Palm and related kernels
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  • Published: 22 February 2007

Invariant measures and disintegrations with applications to Palm and related kernels

  • Olav Kallenberg1 

Probability Theory and Related Fields volume 139, pages 285–310 (2007)Cite this article

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An Erratum to this article was published on 08 May 2007

Abstract

Consider a locally compact group G acting measurably on some spaces S and T. We prove a general representation of G-invariant measures on S and the existence of invariant disintegrations of jointly invariant measures on S × T. The results are applied to Palm and related kernels associated with a stationary random pair (ξ,η), where ξ is a random measure on S and η is a random element in T.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, AL, 36849, USA

    Olav Kallenberg

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  1. Olav Kallenberg
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Corresponding author

Correspondence to Olav Kallenberg.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s00440-007-0071-4

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Cite this article

Kallenberg, O. Invariant measures and disintegrations with applications to Palm and related kernels. Probab. Theory Relat. Fields 139, 285–310 (2007). https://doi.org/10.1007/s00440-006-0053-y

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  • Received: 31 July 2005

  • Revised: 29 November 2006

  • Published: 22 February 2007

  • Issue Date: September 2007

  • DOI: https://doi.org/10.1007/s00440-006-0053-y

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Keywords

  • Invariant measures and kernels
  • Disintegration
  • Skew factorization
  • Absolute continuity
  • Stationary random measures
  • Palm, Campbell, and supporting measures
  • Shift coupling
  • Gibbs and Papangelou kernels

Mathematics Subject Classification (2000)

  • Primary: 28C10
  • Primary: 60G57
  • Secondary: 60G10
  • Secondary: 60G55
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