Approximate Invariance for Ergodic Actions of Amenable Groups
Artikel i vetenskaplig tidskrift, 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.

density theorems

Action sets

aperiodicity

Författare

Michael Björklund

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Alexander Fish

The University of Sydney

DISCRETE ANALYSIS

2397-3129 (eISSN)

6

Ämneskategorier

Algebra och logik

Diskret matematik

Matematisk analys

Mer information

Senast uppdaterat

2019-10-31