On simultaneous local dimension functions of subsets of Rd
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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/
Date of Acceptance: 04/05/2015
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