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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