Strict inequality in the box-counting dimension product formulas

Robinson, James and Sharples, Nicholas ORCID logoORCID: https://orcid.org/0000-0003-1722-5647 (2012) Strict inequality in the box-counting dimension product formulas. Real Analysis Exchange, 38 (1) . pp. 95-120. ISSN 0147-1937 [Article]

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Abstract

We supplement the well known upper and lower box-counting product
inequalities to give a new product formula for subsets of metric spaces. We develop a procedure for constructing sets so that the upper and lower box-counting dimensions of these sets and their product can take arbitrary values satisfying the above product formula. In particular we illustrate how badly behaved both the lower and upper box-counting dimensions can be on taking products.

Item Type: Article
Additional Information: Vol.38 • No. 1 • 2012/2013
Research Areas: A. > School of Science and Technology
Item ID: 18181
Depositing User: Nicholas Sharples
Date Deposited: 15 Oct 2015 11:03
Last Modified: 13 Sep 2022 10:41
URI: https://eprints.mdx.ac.uk/id/eprint/18181

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