Approximate Invariance for Ergodic Actions of Amenable Groups
Journal article, 2019

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 celebrated density theorem for subsets in (Z, +), valid for any countable amenable group, and we show how it can be used to establish a plethora of new inverse product set theorems for upper and lower asymptotic densities. We provide several examples demonstrating that our results are optimal for the settings under study.

aperiodicity

Action sets

density theorems

Author

Michael Björklund

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Alexander Fish

The University of Sydney

DISCRETE ANALYSIS

2397-3129 (eISSN)

6

Subject Categories

Algebra and Logic

Discrete Mathematics

Mathematical Analysis

DOI

10.19086/da.8471

More information

Latest update

8/8/2019 1