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A prevalent transversality theorem for Lipschitz functions


Author: Chris Shannon
Journal: Proc. Amer. Math. Soc. 134 (2006), 2755-2765
MSC (2000): Primary 58C05, 49J52, 90C31; Secondary 58E17
DOI: https://doi.org/10.1090/S0002-9939-06-08607-2
Published electronically: April 13, 2006
MathSciNet review: 2213756
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Abstract: This paper provides a version of the transversality theorem for a class of Lipschitz functions of the form $ f:{\bf R}^n\times C\to {\bf R}^n$, where $ C$ is a convex subset of a normed vector space $ Z$ indexing the parameters in the problem. The set $ C$ may be infinite-dimensional, and the notion of generic used is the measure-theoretic notion of prevalence introduced by Hunt, Sauer and Yorke (1992) and Christensen (1974). This paper also provides some results on sensitivity analysis for solutions to locally Lipschitz equations.


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Additional Information

Chris Shannon
Affiliation: Department of Economics and Department of Mathematics, University of California–Berkeley, Berkeley, California 94720
Email: cshannon@econ.berkeley.edu

DOI: https://doi.org/10.1090/S0002-9939-06-08607-2
Keywords: Prevalence, transversality, Lipschitz functions, nonsmooth analysis
Received by editor(s): April 25, 2003
Published electronically: April 13, 2006
Additional Notes: Thanks to Bob Anderson, Don Brown, Max Stinchcombe and Bill Zame for helpful comments and conversations concerning this paper. The financial support of the National Science Foundation under grant SBR 98-18759, the Miller Institute, and an Alfred P. Sloan Foundation Research Fellowship is gratefully acknowledged.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2006 American Mathematical Society

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