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dc.contributor.authorFraser, Jonathan
dc.contributor.authorHowroyd, Douglas Charles
dc.contributor.authorYu, Han
dc.identifier.citationFraser , J , Howroyd , D C & Yu , H 2018 , ' Dimension growth for iterated sumsets ' , Mathematische Zeitschrift , vol. First Online .
dc.identifier.otherPURE: 256914452
dc.identifier.otherPURE UUID: 8edea8c7-f860-4559-8401-811f1c2a54be
dc.identifier.otherScopus: 85058851244
dc.identifier.otherORCID: /0000-0002-8066-9120/work/58285471
dc.identifier.otherWOS: 000495574800006
dc.descriptionJonathan M. Fraser was financially supported by a Leverhulme Trust Research Fellowship (RF-2016-500) and an EPSRC Standard Grant (EP/R015104/1). Douglas C. Howroyd was financially supported by the EPSRC Doctoral Training Grant (EP/N509759/1). Han Yu was financially supported by the University of St Andrews.en
dc.description.abstractWe study dimensions of sumsets and iterated sumsets and provide natural conditions which guarantee that a set F⊆ℝ satisfies ^dim^BF+F>^dim^BF or even dimHnF→1. Our results apply to, for example, all uniformly perfect sets, which include Ahlfors–David regular sets. Our proofs rely on Hochman’s inverse theorem for entropy and the Assouad and lower dimensions play a critical role. We give several applications of our results including an Erdős–Volkmann type theorem for semigroups and new lower bounds for the box dimensions of distance sets for sets with small dimension.
dc.relation.ispartofMathematische Zeitschriften
dc.rights© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.en
dc.subjectAssouad dimensionen
dc.subjectBox dimensionen
dc.subjectHausdorff dimensionen
dc.subjectDistance seten
dc.subjectQA Mathematicsen
dc.titleDimension growth for iterated sumsetsen
dc.typeJournal articleen
dc.contributor.sponsorThe Leverhulme Trusten
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.description.statusPeer revieweden

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