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.
Type | Article |
---|---|
Title | Strict inequality in the box-counting dimension product formulas |
Authors | Robinson, 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. |
Publisher | Michigan State University Press |
Journal | Real Analysis Exchange |
ISSN | 0147-1937 |
Electronic | 1930-1219 |
Publication dates | |
2012 | |
Publication process dates | |
Deposited | 15 Oct 2015 |
Accepted | 22 Mar 2012 |
Submitted | 22 Sep 2011 |
Output status | Published |
Accepted author manuscript | |
Additional information | Vol.38 • No. 1 • 2012/2013 |
Web address (URL) | https://projecteuclid.org/euclid.rae/1367265642 |
Language | English |
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