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Article | REF: AF218 V1

Fractal Geometry

Author: Jean-Charles PINOLI

Publication date: October 10, 2017

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9. Dimension in Euclidean space...

Above: Dimension in Euclidean space ℝn

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 ℝn...

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