Geometric Measure Theory IV: Rectifiable Sets
Geometry of Euclidean Sets: Vectorial, Topological and Metric Aspects

A rectifiable set is a multidimensional generalization of the classical concept of a rectifiable curve. Rectifiable sets are considered to be generalized continuously differentiable topological manifolds, since they possess properties similar to those of continuously differentiable topological manifolds used in differential geometry (see [AF 207] ).

Definition (rectifiable set). An m-rectifiable subset X of