CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search Norbert Wiener In mathematics , classical Wiener space is the collection of all continuous functions on a given domain (usually a sub- interval of the real line ), taking values in a metric space (usually n -dimensional Euclidean space ). Classical Wiener space is useful in the study of stochastic processes whose sample paths are continuous functions. It is named after the American mathematician Norbert Wiener . 1 Definition 2 Properties of classical Wiener space 2.1 Uniform topology 2.2 Separability and completeness 2.3 Tightness in classical Wiener space 2.4 Classical Wiener measure 3 See also Definition [ edit ] Consider E ⊆ R n and a metric space ( M , d ). The classical Wiener space C ( E ; M ) is the space of all continuous functions f : E → M . I.e. for eve...