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• W2070464931 abstract "Classical ergodic theory deals with measure (or measure class) preserving actions of locally compact groups on Lebesgue spaces. An important tool in this setting is a theorem of Mackey which provides spatial models for BooleanG-actions. We show that in full generality this theorem does not hold for actions of Polish groups. In particular there is no Borel model for the Polish automorphism group of a Gaussian measure. In fact, we show that this group as well as many other Polish groups do not admit any nontrivial Borel measure preserving actions." @default.
• W2070464931 created "2016-06-24" @default.
• W2070464931 creator A5018377073 @default.
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• W2070464931 date "2005-12-01" @default.
• W2070464931 modified "2023-09-27" @default.
• W2070464931 title "The automorphism group of the Gaussian measure cannot act pointwise" @default.
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• W2070464931 doi "https://doi.org/10.1007/bf02775441" @default.
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