Finite generators for countable group actions in the Borel and Baire category settings
@article{Tserunyan2012FiniteGF, title={Finite generators for countable group actions in the Borel and Baire category settings}, author={Anush Tserunyan}, journal={Advances in Mathematics}, year={2012}, volume={269}, pages={585-646} }
11 Citations
Generic Stationary Measures and Actions
- Mathematics
- 2014
Let G be a countably infinite group, and let μ be a generating probability measure on G. We study the space of μ-stationary Borel probability measures on a topological G space, and in particular on…
Krieger’s finite generator theorem for actions of countable groups I
- MathematicsErgodic Theory and Dynamical Systems
- 2020
For an ergodic p.m.p. action $$G \curvearrowright (X, \mu )$$G↷(X,μ) of a countable group G, we define the Rokhlin entropy $$h^{\mathrm {Rok}}_G(X, \mu )$$hGRok(X,μ) to be the infimum of the Shannon…
G R ] 1 4 A ug 2 01 5 Generic Stationary Measures and Actions
- Mathematics
- 2015
Let G be a countably infinite group, and let μ be a generating probability measure on G. We study the space of μ-stationary Borel probability measures on a topological G space, and in particular on…
Krieger's Finite Generator Theorem for Ergodic Actions of Countable Groups.
- Mathematics
- 2015
We continue the study of Rokhlin entropy, an isomorphism invariant for ergodic probability-measure-preserving actions of general countable groups introduced in the previous paper. We prove that every…
Every Borel automorphism without finite invariant measures admits a two-set generator
- MathematicsJournal of the European Mathematical Society
- 2018
We show that if an automorphism of a standard Borel space does not admit finite invariant measures, then it has a two-set generator modulo the sigma-ideal generated by wandering sets. This implies…
Realizations of countable Borel equivalence relations
- Mathematics
- 2019
We study topological realizations of countable Borel equivalence relations, including realizations by continuous actions of countable groups, with additional desirable properties. Some examples…
Borel factors and embeddings of systems in subshifts
- Mathematics
- 2022
In this paper we study the combinatorics of free Borel actions of the group Zd on Polish spaces. Building upon recent work by Chandgotia and Meyerovitch, we introduce property F on Zd-shift spaces X…
RECURRENCE AND THE EXISTENCE OF INVARIANT MEASURES
- MathematicsThe Journal of Symbolic Logic
- 2021
Abstract We show that recurrence conditions do not yield invariant Borel probability measures in the descriptive set-theoretic milieu, in the strong sense that if a Borel action of a locally compact…
BASES FOR NOTIONS OF RECURRENCE
- Mathematics
- 2020
We investigate the existence of non-trivial bases for actions of locally-compact Polish groups satisfying a broad array of recurrence properties.
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