2006/03/08 by Kemal Ilgar Eroğlu, Eroglu, Kemal Ilgar
Mathematics · #28A80 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.math/0603181
openalex publication_date 2006/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that if E is a planar self-similar set with similarity dimension d whose defining maps generate a dense set of rotations, then the d-dimensional Hausdorff measure of the orthogonal projection of E onto any line is zero. We also prove that the radial projection of E centered at any point in the plane also has zero d-dimensional Hausdorff measure. Then we consider a special subclass of these sets and give an upper bound for the Favard length of E(ρ) where E(ρ) denotes the ρ-neighborhood of the set E.