English

Hausdorff Dimension and Hausdorff Measure for Non-integer based Cantor-type Sets

Dynamical Systems 2007-07-02 v1 Metric Geometry

Abstract

We consider digits-deleted sets or Cantor-type sets with β\beta-expansions. We calculate the Hausdorff dimension dd of these sets and show that dd is continuous with respect to β\beta. The dd-dimentional Hausdorff measure of these sets is finite and positive.

Keywords

Cite

@article{arxiv.0706.4343,
  title  = {Hausdorff Dimension and Hausdorff Measure for Non-integer based Cantor-type Sets},
  author = {Qinghe Yin},
  journal= {arXiv preprint arXiv:0706.4343},
  year   = {2007}
}
R2 v1 2026-06-21T08:50:31.213Z