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 , where is a convex subset of a normed vector space indexing the parameters in the problem. The set 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