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 Ban...

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Veröffentlicht in:	Israel journal of mathematics 2017-06, Vol.220 (1), p.175-188
Hauptverfasser:	Bate, David, Csörnyei, Marianna, Wilson, Bobby
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Analysis Applications of Mathematics Banach spaces Dimensional measurement Group Theory and Generalizations Mathematical and Computational Physics Mathematics Mathematics and Statistics Projection Theoretical
Online-Zugang:	Volltext
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Zusammenfassung:	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.
ISSN:	0021-2172 1565-8511
DOI:	10.1007/s11856-017-1514-y