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2016

Invariant measures via inverse limits of finite structures

3 years 16 days ago
Invariant measures via inverse limits of finite structures
Abstract. Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are invariant under all permutations of the underlying set that fix all constants. These measures are constructed from inverse limits of measures on certain finite structures. We use this construction to obtain invariant probability measures concentrated on the classes of countable models of certain first-order theories, including measures that do not assign positive measure to the isomorphism class of any single model. We also characterize those transitive Borel G-spaces admitting a G-invariant probability measure, when G is an arbitrary countable product of symmetric groups on a countable set.
Nathanael Leedom Ackerman, Cameron E. Freer, Jaros
Added 02 Apr 2016
Updated 02 Apr 2016
Type Journal
Year 2016
Where EJC
Authors Nathanael Leedom Ackerman, Cameron E. Freer, Jaroslav Nesetril, Rehana Patel
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