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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An erratum to this article can be found at http://dx.doi.org/10.1007/s00440-007-0071-4
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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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DOI: https://doi.org/10.1007/s00440-006-0053-y
Keywords
- Invariant measures and kernels
- Disintegration
- Skew factorization
- Absolute continuity
- Stationary random measures
- Palm, Campbell, and supporting measures
- Shift coupling
- Gibbs and Papangelou kernels