Plünnecke inequalities for measure graphs with applications

Kamil Bulinski, Alexander Fish

Abstract

We generalize Petridis's new proof of Plünnecke's graph inequality to graphs whose vertex set is a measure space. Consequently, by a recent work of Björklund and Fish, this gives new Plünnecke inequalities for measure preserving actions which enable us to deduce, via a Furstenberg correspondence principle, Banach density estimates in countable abelian groups that improve on those given recently by Jin.