Strict inequality in the box-counting dimension product formulas

Robinson, James and Sharples, Nicholas ORCID: 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. [Article]

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Official URL: https://projecteuclid.org/euclid.rae/1367265642

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
Research Areas:	A. > School of Science and Technology
Item ID:	18181
Depositing User:	Nicholas Sharples
Date Deposited:	15 Oct 2015 11:03
Last Modified:	03 Jun 2019 04:14
URI:	https://eprints.mdx.ac.uk/id/eprint/18181

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