Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces

We present a measure-theoretic condition for a property to hold «almost everywhere» on an infinite-dimensional vector space, with particularemphasis on function spaces such as C k and L p . Like the concept of «Lebesgue almost every» on an infinite-dimensional spaces, our notion of «prevalence» is translation invariant. Instead of using a specific measure on the entire space, we define prevalence in terms of the class of all probability measures with compact support. Prevalence is a more appropriate condition than the topological concepts of «open and dense» or «generic» when one desires a probabilistic result on the likelihood of a given property on a function space

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