A combinatorial proof of Marstrand’s theorem for products of regular Cantor sets

AbstractIn 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