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 -measure in every infinite dimensional separable Banach space whose image under every 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}
}