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

2007/06/29 by Yin, Qinghe
#Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.0706.4343

Abstract

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

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