## Real Analysis Exchange

### Hausdorff capacity and Lebesgue measure

#### 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

https://projecteuclid.org/euclid.rae/1338515219

Mathematical Reviews number (MathSciNet)
MR1433612

Zentralblatt MATH identifier
0879.28005

#### 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

#### References

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• J. Steprāns, Cardinal invariants associated with Hausdorff capacities, Proceeding of the BEST Conferences 1-3, Contemporary Mathematics, 192, AMS, 157–184.