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1996/1997 Hausdorff capacity and Lebesgue measure
Thomas S. Salisbury, Juris Steprāns
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Real Anal. Exchange 22(1): 265-278 (1996/1997).


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.


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Thomas S. Salisbury. Juris Steprāns. "Hausdorff capacity and Lebesgue measure." Real Anal. Exchange 22 (1) 265 - 278, 1996/1997.


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

zbMATH: 0879.28005
MathSciNet: MR1433612

Primary: 28A25

Keywords: bounded difference quotient variation , convex decomposition , integral existence characterization

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 1 • 1996/1997
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