## Real Analysis Exchange

### Metric characterization of pure unrectifiability.

#### Abstract

We show that an analytic subset of the finite dimensional Euclidean space $\real^\dimens$ is purely unrectifiable if and only if the image of any of its compact subsets under every \locquo{} function is a Lebesgue null. We also construct purely unrectifiable compact sets of Hausdorff dimension greater than $1$ which are necessarily sent to finite sets by \locquo{} functions.

#### Article information

Source
Real Anal. Exchange, Volume 31, Number 1 (2005), 195-214.

Dates
First available in Project Euclid: 5 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149516805

Mathematical Reviews number (MathSciNet)
MR2218198

Zentralblatt MATH identifier
1142.26312

Subjects
Primary: 26B05: Continuity and differentiation questions
Secondary: 46B20: Geometry and structure of normed linear spaces

#### Citation

Kun, Gábor; Maleva, Olga; Máthé, András. Metric characterization of pure unrectifiability. Real Anal. Exchange 31 (2005), no. 1, 195--214. https://projecteuclid.org/euclid.rae/1149516805

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