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On simultaneous local dimension functions of subsets of Rd

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dc.contributor.authorOlsen, Lars Ole Ronnow
dc.date.accessioned2015-11-13T09:10:03Z
dc.date.available2015-11-13T09:10:03Z
dc.date.issued2015-09-30
dc.identifier.citationOlsen , L O R 2015 , ' On simultaneous local dimension functions of subsets of R d ' , Bulletin of the Korean Mathematical Society , vol. 52 , no. 5 , pp. 1489-1493 . https://doi.org/10.4134/BKMS.2015.52.5.1489en
dc.identifier.issn1015-8634
dc.identifier.otherPURE: 228697611
dc.identifier.otherPURE UUID: 74b719a1-f995-4464-a8f0-cd7e56521c38
dc.identifier.otherORCID: /0000-0002-8353-044X/work/60630703
dc.identifier.otherWOS: 000363840500007
dc.identifier.otherScopus: 84942936518
dc.identifier.urihttps://hdl.handle.net/10023/7778
dc.descriptionDate of Acceptance: 04/05/2015en
dc.description.abstractFor a subset E ⊑ Rd and x ∈ Rd, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by (Formula presented.) where dimH and dimP denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions f,g: Rd → [0, d] with f ≤ g, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.
dc.format.extent5
dc.language.isoeng
dc.relation.ispartofBulletin of the Korean Mathematical Societyen
dc.rightsCopyright 2015 Korean Mathematical Society. Made available according to the publisher policy under a Creative Commons Attribution - NonCommercial 4.0 (CC BY - NC) licence http://creativecommons.org/licenses/by-nc/4.0/en
dc.subjectHausdorff dimensionen
dc.subjectPacking dimensionen
dc.subjectLocal Hausdorff dimensionen
dc.subjectLocal packing dimensionen
dc.subjectBC Logicen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccBCen
dc.subject.lccQAen
dc.titleOn simultaneous local dimension functions of subsets of Rden
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doihttps://doi.org/10.4134/BKMS.2015.52.5.1489
dc.description.statusPeer revieweden


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