Yet another proof of Marstrand's Theorem

TL;DR

This paper provides a new proof of Marstrand's Theorem, which states that Borel sets in the plane with Hausdorff dimension greater than 1 have projections with positive measure for almost all directions.

Contribution

It introduces an alternative proof of Marstrand's Theorem, extending previous techniques to deepen understanding of geometric measure theory.

Findings

New proof of Marstrand's Theorem established

Techniques extend previous methods in geometric measure theory

Reinforces the theorem's validity for Borel sets with Hausdorff dimension > 1

Abstract

In a paper from 1954 Marstrand proved that if K is a Borel subset of the plane 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 new proof of this theorem, extending the techniques developed in a previous work.