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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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by William Ott and James A. Yorke PDF
Bull. Amer. Math. Soc. 42 (2005), 263-290 Request permission


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:
  • James A. Yorke
  • Affiliation: Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
  • Email:
  • 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
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Bull. Amer. Math. Soc. 42 (2005), 263-290
  • MSC (2000): Primary :, 28C10, 28C15, 28C20; Secondary :, 37C20, 37C45
  • DOI:
  • MathSciNet review: 2149086