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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Prevalence


Authors: William Ott and James A. Yorke
Journal: Bull. Amer. Math. Soc. 42 (2005), 263-290
MSC (2000): Primary :, 28C10, 28C15, 28C20; Secondary :, 37C20, 37C45
Published electronically: March 30, 2005
MathSciNet review: 2149086
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Abstract: Many problems in mathematics and science require the use of infinite-dimensional spaces. Consequently, there is need for an analogue of the finite-dimensional notions of `Lebesgue almost every' and `Lebesgue measure zero' in the infinite-dimensional setting. The theory of prevalence addresses this need and provides a powerful framework for describing generic behavior in a probabilistic way. We survey the theory and applications of prevalence.


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Additional Information

William Ott
Affiliation: Courant Institute of Mathematical Sciences, New York, New York 10012
Email: ott@cims.nyu.edu

James A. Yorke
Affiliation: Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
Email: yorke@ipst.umd.edu

DOI: http://dx.doi.org/10.1090/S0273-0979-05-01060-8
PII: S 0273-0979(05)01060-8
Keywords: Prevalence
Received by editor(s): August 11, 2004
Published electronically: March 30, 2005
Additional Notes: This work is based on an invited talk given by the authors in January 2004 at the annual meeting of the AMS in Phoenix, AZ
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.