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 language | English (US) |
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Pages (from-to) | 405-421 |
Number of pages | 17 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 31 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2011 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics