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arXiv:1801.00325math.FA

Sharp finiteness principles for Lipschitz selections

Charles Fefferman, Pavel Shvartsman

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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.

arXiv comments
57 pages. arXiv admin note: substantial text overlap with arXiv:1708.00811
Journal reference
DOI
Subjects
math.FAFunctional Analysis

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  1. Galactica: an AI trained on humanity's scientific knowledge (by Meta) 1 comment

    • The first thing I tried was "Lipschitz selection", a somewhat overloaded phrase that I encountered a lot in graduate school. I guess I had in mind a summary of this paper: https://arxiv.org/abs/1801.00325 but would have been happy with a description of work related to this…

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