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Lipschitz Images of Haar Null Sets
Author(s) -
Matoušková Eva
Publication year - 2000
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460939900661x
Subject(s) - mathematics , lipschitz continuity , banach space , lebesgue measure , homeomorphism (graph theory) , null set , separable space , pure mathematics , lebesgue integration , real line , unit sphere , mathematics subject classification , discrete mathematics , set (abstract data type) , mathematical analysis , computer science , programming language
Let X be a separable infinite dimensional Banach space. There exist a closed set A ⊂ X which contains a translate of any compact set in the unit ball of X , and a bi‐Lipschitz homeomorphism f of X onto X so that every line in X intersects f ( A ) in a set of Lebesgue measure zero. 1991 Mathematics Subject Classification 46B20.