Geometric and Functional Analysis

, Volume 26, Issue 2, pp 422–477

Finiteness Principles for Smooth Selection

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Abstract

In this paper we prove finiteness principles for \({C^m{({\mathbb{R}^n},{\mathbb{R}^D)}}}\) and \({C^{m-1,1}(\mathbb{R}^n,\mathbb{R}^D)}\) selections. In particular, we provide a proof for a conjecture of Brudnyi-Shvartsman (1994) on Lipschitz selections for the case when the domain is \({X=\mathbb{R}^n}\).

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Charles Fefferman
    • 1
  • Arie Israel
    • 2
  • Garving K. Luli
    • 3
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of MathematicsThe University of Texas at AustinAustinUSA
  3. 3.Department of MathematicsUniversity of California, DavisDavisUSA

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