define rectifiable curve
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A rectifiable curve is a curve having finite length (cf. Line (curve)). More precisely, consider a metric space (X,d) and a continuous function γ:[0,1]→X. γ is a parametrization of a rectifiable curve if there is an homeomorphism φ:[0,1]→[0,1] such that the map γ∘φ is Lipschitz
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In mathematics, a rectifiable set is a set that is smooth in a certain measure-theoretic sense. It is an extension of the idea of a rectifiable curve to higher dimensions; loosely speaking, a rectifiable set is a rigorous formulation of a piece-wise smooth set.
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