On simultaneous local dimension functions of subsets of Rd
MetadataShow full item record
For 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.
Olsen , 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 . DOI: 10.4134/BKMS.2015.52.5.1489
Bulletin of the Korean Mathematical Society
Copyright 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/
DescriptionDate of Acceptance: 04/05/2015
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Showing items related by title, author, creator and subject.
Fraser, Jonathan M. (University of St Andrews, 2013-11-29) - ThesisThe aim of this thesis is to develop the dimension theory of self-affine carpets in several directions. Self-affine carpets are an important class of planar self-affine sets which have received a great deal of attention ...
An analytical, phenomenological and numerical study of geophysical and magnetohydrodynamic turbulence in two dimensions Blackbourn, Luke A. K. (University of St Andrews, 2013-11-29) - ThesisIn this thesis I study a variety of two-dimensional turbulent systems using a mixed analytical, phenomenological and numerical approach. The systems under consideration are governed by the two-dimensional Navier-Stokes ...
The vertical dimensions of the last ice sheet and late quaternary events in northern Ross-shire, Scotland Reed, William J. (University of St Andrews, 1989) - ThesisDespite more than 100 years of research, surprisingly little is known about the precise dimensions of the last ice sheet in Northern Scotland, though recent work has suggested that it may have been much less ...