Invariant Palm and related disintegrations via skew factorization

• 成果类型: Article
• 署名作者: Kallenberg, Olav
• 署名单位: Auburn University System; Auburn University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-009-0254-2
• 发表日期: 2011
• 页码: 279-301
• 关键词: stationary random measures

摘要

Let G be a measurable group with Haar measure., acting properly on a space S and measurably on a space T. Then any sigma-finite, jointly invariant measure M on S x T admits a disintegration nu circle times mu into an invariant measure nu on S and an invariant kernel mu from S to T. Here we construct nu and mu by a general skew factorization, which extends an approach by Rother and Zahle for homogeneous spaces S over G. This leads to easy extensions of some classical propositions for invariant disintegration, previously known in the homogeneous case. The results are applied to the Palm measures of jointly stationary pairs (xi,eta), where xi is a random measure on S and eta is a random element in T.