Open Access
1996/1997 Conditions for equality of Hausdorff and packing measures on ℝ
H. Joyce
Author Affiliations +
Real Anal. Exchange 22(1): 142-152 (1996/1997).


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.


Download Citation

H. Joyce. "Conditions for equality of Hausdorff and packing measures on ℝ." Real Anal. Exchange 22 (1) 142 - 152, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 1 June 2012

zbMATH: 0879.28014
MathSciNet: MR1433602

Primary: 28A75

Keywords: Measure and Integration

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 1 • 1996/1997
Back to Top