Structure theorem for Gaussian measures

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the structure theorem for Gaussian measures shows that the <a href="/facts/Abstract_Wiener_space/eu78QVxt">abstract Wiener space</a> construction is essentially the only way to obtain a <a href="/facts/Strictly_positive_measure/9AJ6rKhM">strictly positive</a> <a href="/facts/Gaussian_measure/WRL0Sdx5">Gaussian measure</a> on a <a href="/facts/Separable_space/2bmU73bk">separable</a> <a href="/facts/Banach_space/sDEIk7EC">Banach space</a>. It was proved in the 1970s by <a href="/facts/Gopinath_Kallianpur/ETmCczVx">Kallianpur</a>–Sato–Stefan and <a href="/facts/Richard_M._Dudley/dAoP1rm2">Dudley</a>–Feldman–<a href="/facts/Lucien_le_Cam/t2DVPly7">le Cam</a>.
</p><p>There is the earlier result due to H. Satô (1969)  which proves that "any Gaussian measure on a separable Banach space is an <a href="/facts/Abstract_Wiener_space/eu78QVxt"> abstract Wiener measure</a> in the sense of <a href="/facts/Leonard_Gross/bITt0dIy"> L. Gross</a>". The result by Dudley et al. generalizes this result to the setting of Gaussian measures on a general <a href="/facts/Topological_vector_space/XRex1ChN">topological vector space</a>.
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Structure theorem for Gaussian measures open-in-new

Structure theorem for Gaussian measures