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. As such, it has many of the desirable properties of smooth manifolds, including tangent spaces that are defined almost everywhere. Rectifiable sets are the underlying object of study in geometric measure theory.
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“I have resolved on an enterprise that has no precedent and will have no imitator. I want to set before my fellow human beings a man in every way true to nature; and that man will be myself.”
—Jean-Jacques Rousseau (1712–1778)