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2005-2006 Metric characterization of pure unrectifiability.
Gábor Kun, Olga Maleva, András Máthé
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Real Anal. Exchange 31(1): 195-214 (2005-2006).


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.


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Gábor Kun. Olga Maleva. András Máthé. "Metric characterization of pure unrectifiability.." Real Anal. Exchange 31 (1) 195 - 214, 2005-2006.


Published: 2005-2006
First available in Project Euclid: 5 June 2006

zbMATH: 1142.26312
MathSciNet: MR2218198

Primary: 26B05
Secondary: 46B20

Keywords: Lipschitz quotient , Purely unrectifiable

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 1 • 2005-2006
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