English

A note on the parameterisation of Besicovitch sets

Classical Analysis and ODEs 2009-01-23 v1

Abstract

In response to a question raised (and answered in the negative) by Terry Tao on his blog as to whether it is possible to rotate a line segment continuously within a set of area zero, we show that there is a set of area zero in the plane within which a line segment can be rotated by a Baire-1 map.

Cite

@article{arxiv.0901.3456,
  title  = {A note on the parameterisation of Besicovitch sets},
  author = {Toby C. O'Neil},
  journal= {arXiv preprint arXiv:0901.3456},
  year   = {2009}
}

Comments

2 pages, no figures

R2 v1 2026-06-21T12:03:35.085Z