Real Analysis Exchange

The Hausdorff dimension of the hyperspace of compact sets

Mark McClure

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

Article information

Real Anal. Exchange, Volume 22, Number 2 (1996), 611-625.

First available in Project Euclid: 22 May 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28A78: Hausdorff and packing measures 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 54B20: Hyperspaces

Fractal Dimensions Hausdorff Measure Hyperspace


McClure, Mark. The Hausdorff dimension of the hyperspace of compact sets. Real Anal. Exchange 22 (1996), no. 2, 611--625.

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