A combinatorial proof of Marstrand's Theorem for products of regular Cantor sets
Dynamical Systems
2020-04-21 v2
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.
Keywords
Cite
@article{arxiv.0911.1191,
title = {A combinatorial proof of Marstrand's Theorem for products of regular Cantor sets},
author = {Yuri Lima and Carlos Gustavo Moreira},
journal= {arXiv preprint arXiv:0911.1191},
year = {2020}
}
Comments
9 pages, 1 figure, referee suggestions incorporated, to appear in Expositiones Mathematicae