Unavoidable sigma-porous sets

We prove that every separable metric space which admits an ℓ1-tree as a Lipschitz quotient has a σ-porous subset which contains every Lipschitz curve up to a set of one-dimensional Hausdorff measure zero. This applies to any Banach space containing ℓ1. We also obtain an infinite-dimensional countere...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 2007-10, Vol.76 (2), p.467-478
Main Author: Maleva, Olga
Format: Article
Language:English
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Summary:We prove that every separable metric space which admits an ℓ1-tree as a Lipschitz quotient has a σ-porous subset which contains every Lipschitz curve up to a set of one-dimensional Hausdorff measure zero. This applies to any Banach space containing ℓ1. We also obtain an infinite-dimensional counterexample to the Fubini theorem for the σ-ideal of σ-porous sets.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms/jdm059