# 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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Abstract Given a Polish space X, a countable Borel equivalence relation E on X, and a Borel cocycle $\rho : E \rightarrow (0, \infty )$, we characterize the circumstances under which there is a…

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Using the orbital approach to the entropy theory we extend from \mathbb{Z}-actions to general countable amenable group actions T (or provide new short proofs for) the following results: (1) the…

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