Porosity, dimension, and local entropies: a survey

Details Porosity, dimension, and local entropies: a survey Porosity, dimension, and local entropies: a survey

2011-10-25

arxiv.org/abs/1110.5682v1

Mathematics

Classical Analysis and ODEs

23 pages, 1 figure

Scientific paper

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.

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