Sharp Finiteness Principles For Lipschitz Selections

Sharp Finiteness Principles For Lipschitz Selections

Let ( M , ρ ) be a metric space and let Y be a Banach space. Given a positive integer m , let F be a set-valued mapping from M into the family of all compact convex subsets of Y of dimension at most m . In this paper we prove a finiteness principle for the existence of a Lipschitz selection of F wit...

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Veröffentlicht in:Geometric and functional analysis 2018-12, Vol.28 (6), p.1641-1705
Hauptverfasser: Fefferman, Charles, Shvartsman, Pavel
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Banach spaces
Mapping
Mathematics
Mathematics and Statistics
Metric space
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Zusammenfassung:Let ( M , ρ ) be a metric space and let Y be a Banach space. Given a positive integer m , let F be a set-valued mapping from M into the family of all compact convex subsets of Y of dimension at most m . In this paper we prove a finiteness principle for the existence of a Lipschitz selection of F with the sharp value of the finiteness constant.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-018-0467-6