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On martingale methods and some Besicovitch type sets

Volume 258 / 2021

Adam Paszkiewicz, Damian Prusinowski 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.

Authors

  • Adam PaszkiewiczFaculty of Mathematics and Computer Science
    University of Lodz
    Stefana Banacha 22
    90-238 Łódź, Poland
    e-mail
  • Damian PrusinowskiFaculty of Mathematics and Computer Science
    University of Lodz
    Stefana Banacha 22
    90-238 Łódź, Poland
    e-mail

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