Aleksandra Kwiatkowska (Department of Mathematics, University of Illinois) Nearactions and their point realizations Abstract: Let (X,m) be the Lebesgue space, and let Aut(X,m) be the group of all measure preserving transformations of X with the natural topology. Given a continuous homomorphism h from a Polish group G to Aut(X,m), it is important to determine if h has a point realization, that is, if it arises from a Borel measure preserving action of G on (X,m). Mackey gave an affirmative answer to this question for G Polish locally compact, and recently Glasner and Weiss, using different methods, gave an affirmative answer for G a closed subgroup of the group of all permutations of natural numbers. In the talk, I will present a common generalization of these two results to a class of groups that includes also, for example, countable products of locally compact groups. This is a joint work with Slawek Solecki. 
