Fractal Geometry : Cartesian products and intersections of fractal objects

Cartesian products and intersections of fractal objects
Fractal Geometry

Author : Jean-Charles PINOLI

Publication date: October 10, 2017 | Lire en français

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17. Cartesian products and intersections of fractal objects

Theorem. The Cartesian product of a subset X of $ℝ^{n}$ and a subset Y of $ℝ^{m}$ has a Hausdorff and Besicovitch dimension satisfying (p. 102 of ):

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Cartesian products and intersections of fractal objects

(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,...

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