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dc.contributor.authorFraser, Jonathan M.
dc.identifier.citationFraser , J M 2014 , ' Assouad type dimensions and homogeneity of fractals ' , Transactions of the American Mathematical Society , vol. 366 , no. 12 , pp. 6687-6733 .
dc.identifier.otherPURE: 159774260
dc.identifier.otherPURE UUID: eb0a09d4-5aee-4f42-80db-6d006b653fa6
dc.identifier.otherWOS: 000344826300017
dc.identifier.otherScopus: 84908391921
dc.identifier.otherORCID: /0000-0002-8066-9120/work/58285467
dc.identifier.otherWOS: 000344826300017
dc.descriptionThe author was supported by an EPSRC Doctoral Training Granten
dc.description.abstractWe investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural 'dimension pair'. In particular, we compute these dimensions for certain classes of self-affine sets and quasi-self-similar sets and study their relationships with other notions of dimension, such as the Hausdorff dimension for example. We also investigate some basic properties of these dimensions including their behaviour regarding unions and products and their set theoretic complexity.
dc.relation.ispartofTransactions of the American Mathematical Societyen
dc.rights© Copyright 2014 American Mathematical Society. First published in Transactions of the American Mathematical Society in Volume 366 (2014), published by the American Mathematical Society. This version may be reproduced under a CC-BY-NC-ND Creative Commons Licence (
dc.subjectAssouad dimensionen
dc.subjectLower dimensionen
dc.subjectSelf-affine carpeten
dc.subjectAhlfors regularen
dc.subjectBaire hierarchyen
dc.subjectSelf-similar setsen
dc.subjectHausdorff dimensionen
dc.subjectPacking dimensionen
dc.subjectAffine fractalsen
dc.subjectQA Mathematicsen
dc.titleAssouad type dimensions and homogeneity of fractalsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.description.statusPeer revieweden

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