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Geometric and Functional Analysis

, Volume 26, Issue 2, pp 422–477 | Cite as

Finiteness Principles for Smooth Selection

  • Charles Fefferman
  • Arie Israel
  • Garving K. Luli
Article

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 \({X=\mathbb{R}^n}\).

Keywords

Strict Inequality Main Lemma Convex Shape Dyadic Cube Doklady Akademii Nauk SSSR 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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