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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
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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 > 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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| Date of first compliant deposit: | 25 October 2019 | ||||||||
| Volume: | 220 | ||||||||
| Number: | 1 | ||||||||
| Page Range: | pp. 175-188 | ||||||||
| DOI: | 10.1007/s11856-017-1514-y | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Publisher Statement: | 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 | ||||||||
| Open Access Version: |
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