Real Analysis Exchange

Hausdorff capacity and Lebesgue measure

Thomas S. Salisbury and Juris Steprāns

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Abstract

It is shown that for any \(r\in (0,1)\) and for any continuous function from the unit interval to itself, there are sets of arbitrarily small Lebesgue measure whose preimage has arbitrarily large \(r\)-Hausdorff capacity. This is generalized to functions from the unit square to the interval.

Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 265-278.

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1338515219

Mathematical Reviews number (MathSciNet)
MR1433612

Zentralblatt MATH identifier
0879.28005

Subjects
Primary: 28A25: Integration with respect to measures and other set functions

Keywords
integral existence characterization bounded difference quotient variation convex decomposition

Citation

Salisbury, Thomas S.; Steprāns, Juris. Hausdorff capacity and Lebesgue measure. Real Anal. Exchange 22 (1996), no. 1, 265--278. https://projecteuclid.org/euclid.rae/1338515219


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References

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