Prevalence
Top Cited Papers
Open Access
- 30 March 2005
- journal article
- Published by American Mathematical Society (AMS) in Bulletin of the American Mathematical Society
- Vol. 42 (03) , 263-291
- https://doi.org/10.1090/s0273-0979-05-01060-8
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.Keywords
This publication has 40 references indexed in Scilit:
- Genericity with Infinitely Many ParametersThe B.E. Journal of Theoretical Economics, 2001
- How projections affect the dimension spectrum of fractal measuresNonlinearity, 1997
- Are the dimensions of a set and its image equal under typical smooth functions?Ergodic Theory and Dynamical Systems, 1997
- Finite fractal dimension and Holder-Lipshitz parametrizationIndiana University Mathematics Journal, 1996
- The Prevalence of Continuous Nowhere Differentiable FunctionsProceedings of the American Mathematical Society, 1994
- Prevalence. An addendum to: “Prevalence: a translation-invariant ‘almost every’ on infinite-dimensional spaces” [Bull. Amer. Math. Soc. (N.S.) 27 (1992), no. 2, 217–238; MR1161274 (93k:28018)]Bulletin of the American Mathematical Society, 1993
- Generic non–existence of equilibria in finance modelsJournal of Mathematical Economics, 1991
- EmbedologyJournal of Statistical Physics, 1991
- The Consumption-Based Capital Asset Pricing ModelEconometrica, 1989
- On the Existence of a Measure Invariant Under a TransformationAnnals of Mathematics, 1939