Pablo Shmerkin
Published 2011-10-25Version 1
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.
Comments: 23 pages, 1 figure
Journal: Rev. Un. Mat. Argentina 52 (2011), no. 2, 81--103
Additive properties of fractal sets on the parabola
On arithmetic sums of fractal sets in ${\Bbb R}^d$
Dimension, entropy, and the local distribution of measures
![QR code for arXiv:1110.5682 [math.CA]](http://oss.arxitics.com/images/favicon.svg)