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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
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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

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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