English

The Besicovitch-Federer projection theorem is false in every infinite dimensional Banach space

Functional Analysis 2018-09-18 v1

Abstract

We construct a purely unrectifiable set of finite H1\mathcal H^1-measure in every infinite dimensional separable Banach space XX whose image under every 0xX0\neq x^*\in X^* has positive Lebesgue measure. This demonstrates completely the failure of the Besicovitch-Federer projection theorem in infinite dimensional Banach spaces.

Keywords

Cite

@article{arxiv.1506.08431,
  title  = {The Besicovitch-Federer projection theorem is false in every infinite dimensional Banach space},
  author = {David Bate and Marianna Csörnyei and Bobby Wilson},
  journal= {arXiv preprint arXiv:1506.08431},
  year   = {2018}
}