# Unavoidable sigma-porous sets

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- Oxford University Press
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- Disciplines

## Abstract

We prove that every separable metric space which admits an l(1)-tree as a Lipschitz quotient has a or-porous subset which contains every Lipschitz curve up to a set of one-dimensional Hausdorff measure zero. This applies to any Banach space containing l(1). We also obtain an infinite-dimensional counterexample to the Fubini theorem for the sigma-ideal of sigma-porous sets.

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