Real Analysis Exchange

Hausdorff capacity and Lebesgue measure

Thomas S. Salisbury and Juris Steprāns

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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

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

First available in Project Euclid: 1 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

integral existence characterization bounded difference quotient variation convex decomposition


Salisbury, Thomas S.; Steprāns, Juris. Hausdorff capacity and Lebesgue measure. Real Anal. Exchange 22 (1996), no. 1, 265--278.

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