On the distance sets of Ahlfors-David regular sets

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dc.contributor.author Orponen, Tuomas
dc.date.accessioned 2020-03-05T14:38:01Z
dc.date.available 2021-12-17T22:02:24Z
dc.date.issued 2017-02-05
dc.identifier.citation Orponen , T 2017 , ' On the distance sets of Ahlfors-David regular sets ' , Advances in Mathematics , vol. 307 , pp. 1029-1045 . https://doi.org/10.1016/j.aim.2016.11.035
dc.identifier.other PURE: 89974946
dc.identifier.other PURE UUID: 94d2a69c-d9a4-41c0-96c8-b1bcbc93b6f3
dc.identifier.other WOS: 000409285300024
dc.identifier.other Scopus: 85001114558
dc.identifier.uri http://hdl.handle.net/10138/313040
dc.description.abstract prove that if empty set not equal K subset of R-2 is a compact s-Ahlfors-David regular set with s >= 1, then dim(p) D(K) = 1, where D(K) := {vertical bar x - y vertical bar : x, y is an element of K} is the distance set of K, and dime stands for packing dimension. The same proof strategy applies to other problems of similar nature. For instance, one can show that if empty set not equal K subset of R-2 is a compact s-Ahlfors David regular set with s >= 1, then there exists a point x(0) is an element of K such that dime K . (K - x(0)) = 1. (C) 2016 Elsevier Inc. All rights reserved. en
dc.format.extent 17
dc.language.iso eng
dc.relation.ispartof Advances in Mathematics
dc.rights cc_by_nc_nd
dc.rights.uri info:eu-repo/semantics/openAccess
dc.subject Distance sets
dc.subject Packing dimension
dc.subject Entropy
dc.subject 111 Mathematics
dc.title On the distance sets of Ahlfors-David regular sets en
dc.type Article
dc.contributor.organization Department of Mathematics and Statistics
dc.description.reviewstatus Peer reviewed
dc.relation.doi https://doi.org/10.1016/j.aim.2016.11.035
dc.relation.issn 0001-8708
dc.rights.accesslevel openAccess
dc.type.version acceptedVersion

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