The Besicovitch–Federer projection theorem is false in every infinite-dimensional Banach space
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.
Unable to display preview. Download preview PDF.
- Y. Benyamini and J. Lindenstrauss, Geometric Nonlinear Functional Analysis, American Mathematical Society Colloquium Publications, Vol. 48, American Mathematical Society, Providence, RI, 2000.Google Scholar
- P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge Studies in Advanced Mathematics, Vol. 44, Cambridge University Press, Cambridge, 1995.Google Scholar