A note on equivalent interval covering systems for Hausdorff dimension on \(\mathbb R\)
type: Item
instance of: scholarly article
title: A note on equivalent interval covering systems for Hausdorff dimension on \(\mathbb R\)
zbMATH Open document ID: 0653.28002
DOI: 10.1155/S016117128800078X
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46303
review text: The Hausdorff dimension of a set in \(\mathbb{R}\) is usually defined by considering countable coverings of the set by general intervals. In this note we establish sufficient conditions under which coverings whose members are restricted to a particular family g of intervals will produce the same value for dimension. A result of Billingsley is then employed to obtain a general technique for computing the dimensions of sets defined by certain types of generalized expansions. A specific example is included.
Mathematics Subject Classification ID: 28A75
Mathematics Subject Classification ID: 28A12
zbMATH DE Number: 4065344
zbMATH Keywords: Vitali covering
zbMATH Keywords: self-similarity
zbMATH Keywords: fractals
zbMATH Keywords: outer Hausdorff measure
zbMATH Keywords: generalized Cantor sets
zbMATH Keywords: Hausdorff dimension
author: Colleen D. Cutler
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4065344