Classifying Cantor Sets by their Fractal Dimensions
Classical Analysis and ODEs
2010-04-13 v2
Abstract
In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovitch and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-Packing measures, for the family of dimension functions h, and characterize this classification in terms of the underlying sequences.
Cite
@article{arxiv.0905.1980,
title = {Classifying Cantor Sets by their Fractal Dimensions},
author = {Carlos A. Cabrelli and Kathryn E. Hare and Ursula M. Molter},
journal= {arXiv preprint arXiv:0905.1980},
year = {2010}
}
Comments
10 pages, revised version. To appear in Proceedings of the AMS.