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Finite curvature of arc length measure implies rectifiability: A new proof

Finite curvature of arc length measure implies rectifiability: A new proof

If E ⊂ C is a set with finite length and finite curvature, then E is rectifiable.This fact, proved by David and Léger in 1999, is one of the basic ingredients for the proof of Vitushkin's conjecture.In this paper we give another different proof of this result.