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2013/2014 Exact Hausdorff Measures of Cantor Sets
Malin Palö
Real Anal. Exchange 39(2): 367-384 (2013/2014).

Abstract

Cantor sets in \(\mathbb{R}\) are common examples of sets for which Hausdorff measures can be positive and finite. 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 \(\mathbb{R}\), 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.

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Malin Palö. "Exact Hausdorff Measures of Cantor Sets." Real Anal. Exchange 39 (2) 367 - 384, 2013/2014.

Information

Published: 2013/2014
First available in Project Euclid: 30 June 2015

zbMATH: 1329.28019
MathSciNet: MR3365381

Subjects:
Primary: 28A78 , 28A80

Keywords: Cantor sets , Hausdorff measures

Rights: Copyright © 2014 Michigan State University Press

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Vol.39 • No. 2 • 2013/2014
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