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arXiv · 1506.08431

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

David Bate·Marianna Csörnyei·Bobby Wilson
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Abstract

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

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David Bate, Marianna Csörnyei, Bobby Wilson. 2015-06-28. The Besicovitch-Federer projection theorem is false in every infinite dimensional Banach space. https://doi.org/10.1007/s11856-017-1514-y

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