Premium
Unavoidable sigma‐porous sets
Author(s) -
Maleva Olga
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm059
Subject(s) - mathematics , lipschitz continuity , hausdorff space , hausdorff measure , counterexample , banach space , metric space , fubini's theorem , quotient , pure mathematics , separable space , discrete mathematics , hausdorff distance , measure (data warehouse) , ideal (ethics) , nowhere dense set , null set , urysohn and completely hausdorff spaces , set (abstract data type) , mathematical analysis , hausdorff dimension , computer science , philosophy , epistemology , database , programming language
We prove that every separable metric space which admits an ℓ 1 ‐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 ℓ 1 . We also obtain an infinite‐dimensional counterexample to the Fubini theorem for the σ‐ideal of σ‐porous sets.