Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T21:00:32.688Z Has data issue: false hasContentIssue false
  • English
  • Français

Rarefaction indices

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

Claude Tricot Jr
Claude Tricot Jr
Affiliation:
Université de Genève, 2–4, rue du Lièvre, Case postale 124, 1211 Genève24, Switzerland
Get access

Extract

There are at least two indices used to measure the size of bounded sets of ℝn of zero measure—Hausdorff dimension (see [4] for a definition), and the density index [7].

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory
Type
Research Article
Information
Mathematika , Volume 27 , Issue 1 , June 1980 , pp. 46 - 57
Copyright
Copyright © University College London 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Billingsley, P.. “Hausdorff dimension in probability theory II”, Illinois J. Math., 5 (1961), 291–298.CrossRefGoogle Scholar
2.Billingsley, P.. Ergodic theory and information (J. Wiley, 1965).Google Scholar
3.Hausdorff, F.. “Dimension und äusseres Mass”, Math. Ann., vol. 79 (1919), 157–179.CrossRefGoogle Scholar
4.Kahane, J.-P. and Salem, R.. Ensembles parfaits et séries trigonometriques (Hermann, Paris, 1963).Google Scholar
5.Rogers, C. A. and Taylor, S. J.. “Functions continuous and singular with respect to a Hausdorff measure”, Mathematika, 8 (1961), 1–31.CrossRefGoogle Scholar
6.Rogers, C. A.. Hausdorff measures (Cambridge University Press, 1970).Google Scholar
7.Tricot, C.. Sur la notion de densité (Cahiers du Département d'econométrie, Gèneve, 1973).Google Scholar