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

Carlos Gustavo Moreira | Lima, Yuri

Keywords: Marstrand's Theorem | Cantor sets | Hausdorff dimension

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.

Anexos:

• marstrand_official.pdf