Real Analysis Exchange

Entropy dimensions of the hyperspace of compact sets

Mark McClure

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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

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

First available in Project Euclid: 3 July 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

fractal dimensions entropy dimension hyperspace


McClure, Mark. Entropy dimensions of the hyperspace of compact sets. Real Anal. Exchange 21 (1995), no. 1, 194--202.

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