AMENABLE ACTIONS AND ALMOST INVARIANT SETS

By Alexander S. Kechris, Todor Tsankov. 2007

61 citations recorded by the source corpus.

In this paper, we study the connections between properties of the action of a countable group Γ on a countable set X and the ergodic theoretic properties of the corresponding generalized Bernoulli shift, i.e., the corresponding shift action of Γ on M^X, where M is a measure space. In particular, we show that the action of Γ on X is amenable iff the shift Γ → M^X has almost invariant sets.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/90c05f7267eb1bf9971496eac72c7fdda68e4ae2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Some topics in the dynamics of group actions on rooted trees (2011, methodology): “For example, the Koopman representation is dealt with in Glasner’s book [67] and in the paper by Kechris and Tsankov [114].”
A SURVEY OF MEASURED GROUP THEORY (2009, background): “with property (T). A SURVEY OF MEASURED GROUP THEORY 43 5. Techniques 5.1. Superrigidity in semi-simple Lie groups. Superrigidity is the following amazing phenomenon discovered by G. A. Margulis (see [82] for more general statements, including products of semi-simple algebraic groups over local ﬁeld”
Entropy for expansive algebraic actions of residually finite groups (2009, background): “Γ is amenable then no action of Γ is strongly ergodic. Corollary 5.4. If Γ is non-amenable then Γy(Xf,µf) is strongly ergodic. Proof. By [LR81], Bernoulli shifts over Γ are strongly ergodic (see also [KT08]). Strong ergodicity is preserved by weak equivalence, so it follows from the previous theorem”
Orbit Equivalence and Measured Group Theory (2010, background): “Kechris-Tsankov [KT08] characterized the generalized Bernoulli shifts Γ y (X0, μ0) V”