A new issue of the Bulletin of the AMS is out, and in it is a fascinating survey article by William Ott and James A. Yorke.
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.The importance of this should be obvious to anyone familiar with the prominence terms like "measure zero" and "almost everywhere" have in Lebesgue measure theory.
Comments