Real Analysis Exchange

Entropy dimensions of the hyperspace of compact sets

Mark McClure

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Abstract

Let \((X,\rho)\) be a metric space, let \((\mathcal{K}(X),\widetilde{\rho})\) denote the space of non-empty compact subsets of \(X\) with the Hausdorff metric, and let \(E \subset X\). The purpose of this paper is to investigate the relationships between the entropy dimensions of \(E\) and of \(\mathcal{K}(E)\).

Article information

Source
Real Anal. Exchange, Volume 21, Number 1 (1995), 194-202.

Dates
First available in Project Euclid: 3 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1341343235

Mathematical Reviews number (MathSciNet)
MR1377529

Zentralblatt MATH identifier
0860.54011

Subjects
Primary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 28D20: Entropy and other invariants 54B20: Hyperspaces

Keywords
fractal dimensions entropy dimension hyperspace

Citation

McClure, Mark. Entropy dimensions of the hyperspace of compact sets. Real Anal. Exchange 21 (1995), no. 1, 194--202. https://projecteuclid.org/euclid.rae/1341343235


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References

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