Open Access
1995/1996 Measure preserving continuous straightenings of fractional dimensional sets
James Foran
Author Affiliations +
Real Anal. Exchange 21(2): 732-738 (1995/1996).


An \(s\)-set in Euclidean space is a set of finite, non-zero, Hausdorff \(s\)-dimensional measure. Call an \(s\)-set straight if its \(s\)-measure agrees with its Method I \(s\)-outer measure. Examples are given where there is a continuous, one-to-one function \(f\) on \(\mathbb{R}^n\) which is measure preserving on \( E\) so that \(f(E)\) is straight (such an \(f\) will be called a straightening of \(E\)). It is shown that any \(s\)-set can be written as a countable union of sets for which there are straightenings.


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James Foran. "Measure preserving continuous straightenings of fractional dimensional sets." Real Anal. Exchange 21 (2) 732 - 738, 1995/1996.


Published: 1995/1996
First available in Project Euclid: 14 June 2012

zbMATH: 0879.28013
MathSciNet: MR1407286

Primary: 28A78

Keywords: Hausdorff dimension , Hausdorff measure

Rights: Copyright © 1995 Michigan State University Press

Vol.21 • No. 2 • 1995/1996
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