Strict inequality in the box-counting dimension product formulas

Article


Robinson, J. and Sharples, N. 2012. Strict inequality in the box-counting dimension product formulas. Real Analysis Exchange. 38 (1), pp. 95-120.
TypeArticle
TitleStrict inequality in the box-counting dimension product formulas
AuthorsRobinson, J. and Sharples, N.
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.

LanguageEnglish
PublisherMichigan State University Press
JournalReal Analysis Exchange
ISSN0147-1937
Electronic1930-1219
Publication dates
Print2012
Publication process dates
Deposited15 Oct 2015
Accepted22 Mar 2012
Submitted22 Sep 2011
Output statusPublished
Accepted author manuscript
Additional information

Vol.38 • No. 1 • 2012/2013

Web address (URL)https://projecteuclid.org/euclid.rae/1367265642
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https://repository.mdx.ac.uk/item/85zq3

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