Nonstandard analysis and the sumset phenomenon in arbitrary amenable groups
Nonstandard analysis and the sumset phenomenon in arbitrary amenable groups
Beiglböck, Bergelson and Fish proved that if subsets $A$, $B$ of a countable discrete amenable group $G$ have positive Banach densities $\alpha$ and $\beta$ respectively, then the product set $AB$ is piecewise syndetic, that is, there exists $k$ such that the union of $k$-many left translates of $AB$ is thick. …