Dimension in Euclidean space...
Fractal Geometry

Article REF: AF218 V1

Dimension in Euclidean space...
Fractal Geometry

Author : Jean-Charles PINOLI

Publication date: October 10, 2017 | Lire en français

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9. Dimension in Euclidean space...

Above: Dimension in Euclidean space $ℝ^{n}$

9.1 Hausdorff and Besicovitch dimensions

Following a construction by C. Carathéodory (1914), F. Hausdorff proposed (1919) a generalization of the notion of dimension taking non-integer values, which was then extensively studied by A. Besicovitch between 1929 and 1937.

Definition (dimension of Hausdorff, 1919, and Besicovitch, 1929, 1934, 1935). The Hausdorff and Besicovitch dimension of a non-zero subset X of $ℝ^{n}$ ...

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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...

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