Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T23:08:05.527Z Has data issue: false hasContentIssue false
  • English
  • Français

On some regularity conditions of Borel measures on R

Part of: Classical measure theory Stochastic processes

Published online by Cambridge University Press:  09 April 2009

F. Ben Nasr
F. Ben Nasr
Affiliation:
Faculté des Sciences de Monastir Départment de Mathématiques 5000 Monastir, Tunisie
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The aim of this paper is to resolve Taylor's question concerning certain regularity conditions on a Borel measure. The proposed solution is given in the framework of Brown, Michon and Peyrière, and Olsen.

Keywords

Hausdorff dimensionpacking dimension.

MSC classification

Secondary: 28A60: Measures on Boolean rings, measure algebras 60G57: Random measures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 63 , Issue 2 , October 1997 , pp. 218 - 224
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Nasr, F. Ben, ‘Calcul de dimensions de packing’, Colloq. Math. 71 (1996), 137–148.CrossRefGoogle Scholar
[2]Billingsley, P., Ergodic theory and information (Wiley, New York, 1965).Google Scholar
[3]Brown, G., Michon, G. and Peyriere, J., ‘On the multifractal analysis of measures’, J. Statist. Phys. 66 (1992), 775–790.CrossRefGoogle Scholar
[4]Olsen, L., ‘A multifractal formalism’, Adv. Math. 116 (1996), 82–196.CrossRefGoogle Scholar
[5]Peyriere, J., ‘Multifractal measures’, in: NATO Adv. Study Inst. Ser. C 372 (Nijhoff, Dordrecht, 1992) pp. 175–186.Google Scholar
[6]Taylor, S. J., ‘The fractal analysis of Borel measures in R d’, J. Fourier Anal. Appl., to appear.Google Scholar
[7]Tricot, C., ‘Two definitions of fractional dimension’, Math. Proc. Cambridge Philos. Soc. 91 (1982), 57–74.CrossRefGoogle Scholar