Combinatorial properties of the Hausdorff dimension
type: Item
instance of: scholarly article
title: Combinatorial properties of the Hausdorff dimension
zbMATH Open document ID: 0709.11041
DOI: 10.1016/0378-3758(89)90042-6
published in: Journal of Statistical Planning and Inference
publication date: 1989-01-01T00:00:00Z
review text: The author considers subsets F of \(X^{\omega}\), the space of infinite sequences over an alphabet of cardinality r. Introducing a suitable entropy \(H_ F\) for such sets (in terms of combinatorial properties) he shows that, for a certain class of such sets, \(H_ F\) equals the Hausdorff dimension of the set obtained by interpreting each \(x\in F\) as the base r expansion of a real number.
Mathematics Subject Classification ID: 11K55
Mathematics Subject Classification ID: 68Q45
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 4164979
zbMATH Keywords: channel capacity
zbMATH Keywords: structure function
zbMATH Keywords: alphabet
zbMATH Keywords: entropy
zbMATH Keywords: Hausdorff dimension
author: Ludwig Staiger
reviewed by: Bodo Volkmann
MaRDI profile type: Publication
full work available at URL: 0378-3758(89)90042-6
OpenAlex ID: W1998090580
cites work: Q5515914
cites work: Billingsley dimension in probability spaces
cites work: The Capacity and Ambiguity of a Transducer
cites work: On the entropy of context-free languages
cites work: A Mathematical Theory of Communication
cites work: Q3332917
cites work: Q3707909
cites work: Über Hausdorffsche Dimensionen von Mengen, die durch Zifferneigenschaften charakterisiert sind. V
cites work: Q3832612
description: scientific article; zbMATH DE number 4164979