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2000/2001 Typical Properties of Lipschitz Functions
Philip D. Loewen, Xianfu Wang
Real Anal. Exchange 26(2): 717-726 (2000/2001).


In terms of Baire category, a typical real-valued Lipschitz function on a finite dimensional space has a local minimum at every point of a dense subset of the domain, and a Dini subdifferential that is either singleton or empty at all points. Moreover, its Dini subdifferential is empty outside a set of first category. Hence a typical Lipschitz function has no points of subdifferential regularity.


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Philip D. Loewen. Xianfu Wang. "Typical Properties of Lipschitz Functions." Real Anal. Exchange 26 (2) 717 - 726, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 27 June 2008

zbMATH: 1053.49015
MathSciNet: MR1844388

Primary: 49J52

Keywords: Baire category , dense minimizers , Dini subdifferential , Lipschitz function , nonangularity , subdifferential regularity

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 2 • 2000/2001
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