Spatial models of Boolean actions and groups of isometries

Aleksandra Kwiatkowska, Sławomir Solecki

Research output: Contribution to journalArticle

Abstract

Given a Polish group G of isometries of a locally compact separable metric space, we prove that each measure-preserving Boolean action by G has a spatial model or, in other words, has a point realization. This result extends both a classical theorem of Mackey and a recent theorem of Glasner and Weiss, and it covers interesting new examples. In order to prove our result, we give a characterization of Polish groups of isometries of locally compact separable metric spaces which may be of independent interest. The solution to Hilbert's fifth problem plays an important role in establishing this characterization.

Original languageEnglish (US)
Pages (from-to)405-421
Number of pages17
JournalErgodic Theory and Dynamical Systems
Volume31
Issue number2
DOIs
StatePublished - Apr 1 2011

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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