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Plünnecke inequalities for measure graphs with applications

Published online by Cambridge University Press:  06 October 2015

KAMIL BULINSKI Open the ORCID record for KAMIL BULINSKI [Opens in a new window]  and
ALEXANDER FISH
KAMIL BULINSKI
Affiliation:
School of Mathematics and Statistics, University of Sydney, Australia email [email protected], [email protected]
ALEXANDER FISH
Affiliation:
School of Mathematics and Statistics, University of Sydney, Australia email [email protected], [email protected]
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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 extend those given by Jin.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 2 , April 2017 , pp. 418 - 439
Copyright
© Cambridge University Press, 2015 

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