Abstract. I will present a result showing that each measure preserving Boolean action of a Polish group of isometries of a locally compact separable metric space has a spatial model or, in other words, has a point realization. This result extends a classical theorem of Mackey and a recent theorem of Glasner and Weiss. The proof of the result requires a new characterization of Polish groups of isometries of locally compact separable metric spaces which may be of independent interest, and which I will also present. The solution to Hilbert's fifth problem plays an important role in establishing this characterization. This is a joint work with Aleksandra Kwiatkowska.
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