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

Article REF: AF222 V1

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

Author : Jean-Charles PINOLI

Publication date: May 10, 2026 | Lire en français

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13. Geometric Measure Theory IV: Rectifiable Sets

13.1 Grindable Assemblies

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 $ℝ_{2}^{n}$ ...

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Bibliography

(1) - AUBIN (J.P.), FRANKOWSKA (H.) - Set-Valued Analysis, - Birkhäuser (1990).
(2) - BERGER (M.) - Geometry, - Springer, vol. 1 and 2, [1st ed., 1987] (2009).
(3)...

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