Metric characterization of pure unrectifiability. (English) Zbl 1142.26312
Summary: We show that an analytic subset of the finite dimensional Euclidean space \(\mathbb R^m\) is purely unrectifiable if and only if the image of any of its compact subsets under every local Lipschitz quotient 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 local Lipschitz quotient functions.
MSC:
| 26B05 | Continuity and differentiation questions |
| 46B20 | Geometry and structure of normed linear spaces |
References:
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