Real Analysis Exchange

Conditions for equality of Hausdorff and packing measures on ℝ

H. Joyce

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This note answers the question, for which Hausdorff functions \(h\) may the \(h\)-Hausdorff and \(h\)-packing measures agree on some subset \(A\) of \(\mathbb{R}^n\), and be positive and finite. We show that these conditions imply that \(h\) is a regular density function, in the sense of Preiss, and that for each such function there is a subset of \(\mathbb{R}^n\) on which the \(h\)-Hausdorff and \(h\)-packing measures agree and are positive and finite.

Article information

Real Anal. Exchange, Volume 22, Number 1 (1996), 142-152.

First available in Project Euclid: 1 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28A75: Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]

Measure and Integration


Joyce, H. Conditions for equality of Hausdorff and packing measures on ℝ. Real Anal. Exchange 22 (1996), no. 1, 142--152.

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