Real Analysis Exchange
- Real Anal. Exchange
- Volume 22, Number 1 (1996), 265-278.
Hausdorff capacity and Lebesgue measure
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.
Real Anal. Exchange, Volume 22, Number 1 (1996), 265-278.
First available in Project Euclid: 1 June 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 28A25: Integration with respect to measures and other set functions
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