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Porosity, dimension, and local entropies: a survey

Shmerkin, P (2011) Porosity, dimension, and local entropies: a survey Revista de la Union Matematica Argentina, 52 (2). 81 - 103. ISSN 1669-9637

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Abstract

Porosity and dimension are two useful, but different, concepts that quantify the size of fractal sets and measures. An active area of research concerns understanding the relationship between these two concepts. In this article we will survey the various notions of porosity of sets and measures that have been proposed, and how they relate to dimension. Along the way, we will introduce the idea of local entropy averages, which arose in a different context, and was then applied to obtain a bound for the dimension of mean porous measures.

Item Type: Article
Additional Information: Published in Revista de la Union Matematica Argentina. This is an open access journal, meaning it is freely available on the public internet, permitting any users to read, download, copy, distribute, print, search, or link to the full texts of these articles, crawl them for indexing, pass them as data to software, or use them for any other lawful purpose, without financial, legal, or technical barriers other than those inseparable from gaining access to the internet itself.
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Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Symplectic Elements
Date Deposited: 27 Jan 2012 10:03
Last Modified: 23 Sep 2013 19:01
URI: http://epubs.surrey.ac.uk/id/eprint/121089

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