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

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

2007-06-29

arxiv.org/abs/0706.4343v1

Mathematics

Dynamical Systems

Scientific paper

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

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