A classification of orbits admitting a unique invariant measure

Nathanael Ackerman,Cameron Freer,Aleksandra Kwiatkowska,Rehana Patel

doi:10.1016/j.apal.2016.08.003

A classification of orbits admitting a unique invariant measure

Nathanael Ackerman, Cameron Freer + Show 2 more

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https://doi.org/10.1016/j.apal.2016.08.003

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Journal: Annals of Pure and Applied Logic	Publication Date: Aug 24, 2016
Citations: 11	License type: publisher-specific-oa

Affiliation: Harvard University, Massachusetts Institute of Technology, University of Bonn, University of Wrocław, Franklin W. Olin College of Engineering

#Countable Language #Isomorphism Class + Show 8 more

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Abstract

We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability measures on this space that are S∞-invariant and concentrated on a single isomorphism class must be zero, or one, or continuum. Further, such an isomorphism class admits a unique S∞-invariant probability measure precisely when the structure is highly homogeneous; by a result of Peter J. Cameron, these are the structures that are interdefinable with one of the five reducts of the rational linear order (Q,<).

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