Real Analysis Exchange

Packing Measure in General Metric Space

G. A. Edgar

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Abstract

Packing measures are counterparts to Hausdorff measures, used in measuring fractal dimension of sets. C. Tricot defined them for subsets of finite-dimensional Euclidean space. We consider here the proper way to phrase the definitions for use in general metric spaces, and for Hausdorff functions other than the simple powers, in particular non-blanketed Hausdorff functions. The question of the Vitali property arises in this context. An example of a metric space due to R. O. Davies illustrates the concepts.

Article information

Source
Real Anal. Exchange, Volume 26, Number 2 (2000), 831-852.

Dates
First available in Project Euclid: 27 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1214571371

Mathematical Reviews number (MathSciNet)
MR1844397

Zentralblatt MATH identifier
1010.28007

Subjects
Primary: 28A80: Fractals [See also 37Fxx]
Secondary: 26A39: Denjoy and Perron integrals, other special integrals

Keywords
fractal measure packing measure Davies space Vitali property

Citation

Edgar, G. A. Packing Measure in General Metric Space. Real Anal. Exchange 26 (2000), no. 2, 831--852. https://projecteuclid.org/euclid.rae/1214571371


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