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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
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 | ||||||||
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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: |
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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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