We generalize Petridis's new proof of Pl\"unnecke's graph inequality to
graphs whose vertex set is a measure space. Consequently, this gives new
Pl\"unnecke 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 by Jin.Comment: 24 pages, 1 figur
