Sharp finiteness principles for Lipschitz selections

2017/12/31 by Fefferman, Charles, Shvartsman, Pavel
#46E35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1801.00325

Abstract

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.

Related

• Sharp finiteness principles for Lipschitz selections: long version
• On the Core of a Low Dimensional Set-Valued Mapping
• The Core of a 2-Dimensional Set-Valued Mapping. Existence Criteria and Efficient Algorithms for Lipschitz Selections of Low Dimensional Set-Valued Mappings
• Existence Criteria for Lipschitz Selections of Set-Valued Mappings in \bf R²
• A Pointwise Lipschitz Selection Theorem