Abstract Wiener space | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-27

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Abstract_Wiener_space


00:00:35 1 Definition
00:01:34 2 Properties
00:02:08 3 Example: Classical Wiener space
00:03:44 4 See also
00:03:50 5 References
00:06:15 See also



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SUMMARY
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An abstract Wiener space is a mathematical object in measure theory, used to construct a "decent" (strictly positive and locally finite) measure on an infinite-dimensional vector space.  It is named after the American mathematician Norbert Wiener.  Wiener's original construction only applied to the space of real-valued continuous paths on the unit interval, known as classical Wiener space; Leonard Gross provided the generalization to the case of a general separable Banach space.
The structure theorem for Gaussian measures states that all Gaussian measures can be represented by the abstract Wiener space construction.