6. Regularity of curves and surfaces

A curve or surface is said to be regular if its behavior is not pathological according to the mathematical frame of reference used (e.g. differentiability or rectifiability).

6.1 Grindability

Definition (rectifiability). A non-empty subset of $ℝ^{n}$ $μ_{H}_{n}^{m}$ -mesurable is (countably) m-rectifiable if there exists a countable number of Lipchitzian applications

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Regularity of curves and surfaces

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Bibliography

(1) - AARTS (J.M.), NISHIURA (T.) - Dimension and extensions, - North-Holland, 331 pages (1993).
(2) - ALBEVERIO (S.), PRATSIOVYTYL (M.), TORBIN (G.) - Transformations preserving the Hausdorff-Besicovitch dimension, - Central European Journal...