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arXiv · 0911.1191

A combinatorial proof of Marstrand's Theorem for products of regular Cantor sets

Yuri Lima·Carlos Gustavo Moreira
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Abstract

In 1954 Marstrand proved that if K is a subset of R^2 with Hausdorff dimension greater than 1, then its one-dimensional projection has positive Lebesgue measure for almost-all directions. In this article, we give a combinatorial proof of this theorem when K is the product of regular Cantor sets of class C^{1+a}, a>0, for which the sum of their Hausdorff dimension is greater than 1.

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Yuri Lima, Carlos Gustavo Moreira. 2009-11-06. A combinatorial proof of Marstrand's Theorem for products of regular Cantor sets. https://doi.org/10.1016/j.exmath.2011.01.003

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