Exact Hausdorff measures of Cantor sets
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Publication:2356306
DOI10.14321/REALANALEXCH.39.2.0367zbMATH Open1329.28019arXiv1705.00858OpenAlexW3155339393MaRDI QIDQ2356306
Author name not available (Why is that?)
Publication date: 29 July 2015
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1705.00858
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