Related papers: Hyperfinite actions on countable sets and probabil…

We extend the classical Baire category approach, used in proving the finite generator theorem of Krieger, the homomorphism theorem of Sinai and the isomorphism theorem of Ornstein, applying a similar reasoning to the case of actions of…

We investigate the possibility of replacing the topology of convergence in probability with convergence in $L^1$. A characterization of continuous linear functionals on the space of measurable functions is also obtained.

We prove that for certain actions of a discrete countable residually finite amenable group acting on a compact metric space with specification property, periodic measures are dense in the set of invariant measures.

We prove that if an ergodic action of a countable group on a probability space admits a generating partition having finite Shannon entropy then it admits a finite generating partition.

We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a…

We consider several weaker versions of the notion of conjugacy and orbit equivalence of measure preserving actions of countable groups on probability spaces, involving equivalence of the ultrapower actions and asymptotic intertwining…

We study a positive-definite function associated to a measure-preserving equivalence relation on a standard probability space and use it to measure quantitatively the proximity of subequivalence relations. This is combined with a recent…

We consider an action of a countable amenable group on a compact metric space, focusing on the set of generic points with respect to a fixed F{\o}lner sequence. For a given characteristic class, we prove that the set of points that are…

We examine the selective screenability property in topological groups. In the metrizable case we also give characterizations in terms of the Haver property and finitary Haver property respectively relative to left-invariant metrics. We…

In the present paper our main objective is to extend the notion of $D$-sets in countable amenable groups and to discuss its connection with weak mixing for amenable group actions. Further we prove that *-notions are equivalent in the…

The notion of a semitransitive binary action of a group $G$ on a topological space is introduced. A duality theorem is proved, establishing a bijective correspondence between semitransitive distributive binary $G$-spaces and topological…

We study analytic properties of graph product of finite groups with a hyperbolic defining graph. This is done by studying dynamics on the Bowditch compactification of the extension graph, or the crossing graph, of graph product. In…

This is a survey on upper and lower bounds for finite group actions on bounded surfaces, 3-dimensional handlebodies and closed handles, handlebodies in arbitrary dimensions and finite graphs (the common feature of these objects is that all…

We develop in this paper some general techniques to analyze action sets of small doubling for probability measure-preserving actions of amenable groups. As an application of these techniques, we prove a dynamical generalization of Kneser's…

The goal of this paper is threefold. First, we describe the notion of dissociation for closed subgroups of the group of permutations on a countably infinite set and explain its numerous consequences on unitary representations…

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…

We describe conditions that characterize amenability for groups in terms of positive definite functions valued in a von Neumann algebra.

We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such…

In this paper, we define a set which has a finite group action and is generated by a finite color set, a set which has a finite group action, and a subset of the set of non negative integers. we state its properties to apply one of solution…

We construct measures on definable sets in $e$-free perfect PAC fields, as well as on perfect PAC fields whose absolute Galois groups are free pro-$p$ of finite rank. We deduce the definable amenability of all groups definable in such…