Israel Journal of Mathematics

, Volume 220, Issue 1, pp 175–188 | Cite as

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

  • David Bate
  • Marianna CsörnyeiEmail author
  • Bobby Wilson


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


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© Hebrew University of Jerusalem 2017

Authors and Affiliations

  1. 1.Department of MathematicsThe University of ChicagoChicagoUSA

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