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Journal of the London Mathematical Society Advance Access originally published online on October 18, 2007
Journal of the London Mathematical Society 2007 76(2):467-478; doi:10.1112/jlms/jdm059
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© 2007 London Mathematical Society

Unavoidable sigma-porous sets

Olga Maleva

Department of Mathematics
University College London
Gower Street
London
WC1E 6BT
United Kingdom
olga@math.ucl.ac.uk
Current address:
MathematicsInstitute
University of Warwick
Coventry
CV4 7AL
United Kingdom

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

2000 Mathematics Subject Classification 28A05 (primary), 46B20, 46G99 (secondary).

The author was supported by the Marie Curie Intra-European Fellowship, contract no. MEIF-CT-2003-501214.

Received November 26, 2005; published online October 18, 2007.


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