Structure theorem for Gaussian measures
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In mathematics, the structure theorem for Gaussian measures shows that the abstract Wiener space construction is the only way to obtain a Gaussian measure on a separable Banach space. It was proved in 1977 by Kallianpur-Sato-Stefan and Dudley-Feldman-le Cam.
[edit] Statement of the theorem
Let γ be a strictly positive Gaussian measure on a separable Banach space E. Then there exists a separable Hilbert space H and a map 
such that is an abstract Wiener space with 
, where γH is the canonical Gaussian cylinder set measure on H.
