Bate, David, Csornyei, Marianna and Wilson, Bobby (2017) The Besicovitch Federer projection theorem is false in every infinite dimensional Banach space. Israel Journal of Mathematics, 220 (1). pp. 175-188. doi:10.1007/s11856-017-1514-y ISSN 0021-2172.

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Abstract

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Banach spaces, Measure theory, Nonlinear functional analysis
Journal or Publication Title:	Israel Journal of Mathematics
Publisher:	Magnes Press
ISSN:	0021-2172
Official Date:	June 2017
Dates:	Date Event June 2017 Published 5 May 2017 Available 12 December 2015 Accepted
Volume:	220
Number:	1
Page Range:	pp. 175-188
DOI:	10.1007/s11856-017-1514-y
Status:	Peer Reviewed
Publication Status:	Published
Reuse Statement (publisher, data, author rights):	This is a post-peer-review, pre-copyedit version of an article published in Israel Journal of Mathematics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11856-017-1514-y
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	25 October 2019
Date of first compliant Open Access:	29 October 2019
Open Access Version:	ArXiv

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