# Exact Hausdorff Measures of Cantor Sets Journal article, 2014

Cantor sets in R are common examples of sets for which Hausdorff measures can be positive and fnite. However, there exist Cantor sets for which no Hausdorff measure is supported and finite. The purpose of this paper is to try to resolve this problem by studying an extension of the Hausdorff measures $\mu_h$ on on $\mathbb{R}$, allowing gauge functions to depend on the midpoint of the covering intervals instead of only on the diameter. As a main result, a theorem about the Hausdorff measure of any regular enough Cantor set, with respect to a chosen gauge function, is obtained.

## Author

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

#### Real Analysis Exchange

0147-1937 (ISSN)

Vol. 39 2 367-384

Basic sciences

#### Subject Categories

Discrete Mathematics

Mathematical Analysis