On martingale methods and some Besicovitch type sets
Volume 258 / 2021
Studia Mathematica 258 (2021), 221-233
MSC: Primary 60G42, 28A05; Secondary 60F15, 26A48.
DOI: 10.4064/sm200319-18-6
Published online: 17 December 2020
Abstract
A set $B \subset \mathbb R ^2$ is a Besicovitch set if $B$ is a Borel null set and $B$ contains a unit interval in any direction. We show that the existence of Besicovitch sets is a natural consequence of the Doob martingale convergence theorem.
