On simultaneous local dimension functions of subsets of Rd

Lars Ole Ronnow Olsen

doi:10.4134/BKMS.2015.52.5.1489

On simultaneous local dimension functions of subsets of R^d

Lars Ole Ronnow Olsen

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For a subset E ⊑ R^d and x ∈ R^d, 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 dim_H and dim_P 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: R^d → [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.

Original language	English
Pages (from-to)	1489-1493
Number of pages	5
Journal	Bulletin of the Korean Mathematical Society
Volume	52
Issue number	5
DOIs	https://doi.org/10.4134/BKMS.2015.52.5.1489
Publication status	Published - 30 Sept 2015

Keywords

Hausdorff dimension
Packing dimension
Local Hausdorff dimension
Local packing dimension

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10.4134/BKMS.2015.52.5.1489

BKMS-52-5-1489-1493
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/
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Cite this

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