A Boolean action of \(C(M, U(1))\) without a spatial model and a re-examination of the Cameron-Martin theorem

DOI10.1016/J.JFA.2012.08.004zbMath1253.37014arXiv1201.3947OpenAlexW2039661070MaRDI QIDQ1762339

Justin Tatch Moore, Slawomir Solecki

Publication date: 23 November 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.3947

zbMATH Keywords

group actioninfinite-dimensionalPolish groupspatial modelBoolean actionCameron-Martinpoint realizationwhirly

Mathematics Subject Classification ID

General groups of measure-preserving transformations (28D15) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items (3)

The spectral form of Koopman representations of the group of measurable functions with values in the circle ⋮ An uncountable Furstenberg–Zimmer structure theory ⋮ Unitary representations of the groups of measurable and continuous functions with values in the circle

Cites Work

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• The automorphism group of the Gaussian measure cannot act pointwise
• Point realizations of transformation groups
• Spatial models of Boolean actions and groups of isometries
• On the small balls problem for equivalent Gaussian measures
• Spatial and non-spatial actions of Polish groups
• Ergodic Theory
• Concentration of measure and whirly actions of Polish groups

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