Metric Characterization of Pure Unrectifiability
نویسندگان
چکیده
We show that an analytic subset of the finite dimensional Euclidean space R 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.
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