English

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.

Keywords

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.

R2 v1 2026-06-21T13:01:30.127Z