Real Analysis Exchange

Multifractal variation measures and multifractal density theorems.

J. Cole and L. Olsen

Full-text: Open access

Abstract

In this paper we show that the multifractal Hausdorff measure and multifractal packing measure introduced by Olsen and Peyriere can be expressed as Henstock-Thomson \lq\lq variation" measures. As an application we prove a density theorem for these two measures that extends results by Edgar and is more refined than those found in [Ol1].

Article information

Source
Real Anal. Exchange, Volume 28, Number 2 (2002), 501-514.

Dates
First available in Project Euclid: 20 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.rae/1184963813

Mathematical Reviews number (MathSciNet)
MR2010333

Zentralblatt MATH identifier
1051.28004

Subjects
Primary: 28A80: Fractals [See also 37Fxx]

Keywords
Fractals multifractals Hausdorff measure packing measure Henstock-Thomson ``variation" measures densities

Citation

Cole, J.; Olsen, L. Multifractal variation measures and multifractal density theorems. Real Anal. Exchange 28 (2002), no. 2, 501--514. https://projecteuclid.org/euclid.rae/1184963813


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