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

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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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Official URL: https://doi.org/10.1007/s11856-017-1514-y

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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:
DateEvent
June 2017Published
5 May 2017Available
12 December 2015Accepted
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:
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