Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the notions of prevalence and shyness are notions of "almost everywhere" and "measure zero" that are well-suited to the study of infinite-dimensional spaces and make use of the translation-invariant Lebesgue measure on finite-dimensional real spaces. The term "shy" was suggested by the American mathematician John Milnor. Let V be a real topological vector space and let S be a Borel-measurable subset of V. S is said to be prevalent if there exists a finite-dimensional subspace P of V, called the probe set, such that v + p S for all v V and P-almost all p P, where P denotes the dim(P)-dimensional Lebesgue measure on P. Put another way, for every v V, Lebesgue-almost every point of the hyperplane v + P lies in S. A non-Borel subset of V is said to be prevalent if it contains a prevalent Borel subset.

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