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Quasi-invariant measures for continuous group actions

Kechris, Alexander S. (2020) Quasi-invariant measures for continuous group actions. In: Trends in Set Theory. Contemporary Mathematics. No.752. American Mathematical Society , Providence, RI, pp. 113-119. ISBN 978-1-4704-4332-0.

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The class of ergodic, invariant probability Borel measure for the shift action of a countable group is a G_δ set in the compact, metrizable space of probability Borel measures. We study in this paper the descriptive complexity of the class of ergodic, quasi-invariant probability Borel measures and show that for any infinite countable group Γ it is Π⁰₃-hard, for the group Z it is Π⁰₃-complete, while for the free group F_∞ with infinite, countably many generators it is Π⁰_α-complete, for some ordinal α with 3 ≤ α ≤ ω +2. The exact value of this ordinal is unknown.

Item Type:Book Section
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Additional Information:© 2020 American Mathematical Society. The author was partially supported by NSF grant DMS-1464475.
Funding AgencyGrant Number
Subject Keywords:group actions, invariant measures, quasi-invariant measures, ergodic measures
Series Name:Contemporary Mathematics
Issue or Number:752
Classification Code:2010 Mathematics Subject Classification: Primary 03C13, Secondary 03C15, 05D10, 37B05, 37A15, 54H20
Record Number:CaltechAUTHORS:20210707-142840752
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109734
Deposited By: Tony Diaz
Deposited On:08 Jul 2021 16:55
Last Modified:16 Nov 2021 19:37

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