A combinatorial proof of Marstrand’s theorem for products of regular Cantor sets |
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Authors: | Yuri Lima Carlos Gustavo Moreira |
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Institution: | a Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil |
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Abstract: | In a paper from 1954 Marstrand proved that if K⊂R2 has a Hausdorff dimension greater than 1, then its one-dimensional projection has a 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 C1+α, α>0, for which the sum of their Hausdorff dimension is greater than 1. |
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Keywords: | Cantor sets Hausdorff dimension Marstrand theorem |
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