Exact Hausdorff measures of Cantor sets
type: Item
instance of: scholarly article
title: Exact Hausdorff measures of Cantor sets
zbMATH Open document ID: 1329.28019
author: Malin Palö
published in: Real Analysis Exchange
publication date: 2015-07-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1705.00858
full work available at URL: https://projecteuclid.org/euclid.rae/1435670002
review text: The author investigates Hausdorff measures \(\mu_h\) on Cantor sets, i.e., compact, perfect, and totally disconnected subsets of \(\mathbb{R}\), where the gauge function \(h\) not only depends on the length of the covering intervals but also on their midpoints. For a class of regular enough Cantor sets it is shown that under this additional assumption a formula for the Hausdorff measure can be obtained. For three examples, the exact Hausdorff measure is computed.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 6467133
zbMATH Keywords: Cantor sets
zbMATH Keywords: Hausdorff measure
reviewed by: Peter Massopust
MaRDI profile type: Publication
OpenAlex ID: W3155339393
arXiv ID: 1705.00858
DOI: 10.14321/REALANALEXCH.39.2.0367
description: scientific article