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I'm looking for some simple proofs for the fact that on $(C[0,T],F(C([0,T])),P_{*})$ where $F$ represents Borel Sigma algebra , $P_{*}$ the Wiener Measure , then how to proove that $P_{*}$ measure is a Gaussian Measure on the Banach Space and its sigma algebra pair $(C[0,T],F(C([0,T])))$ .Here $C[0,T]$ denotes space of continuous Functions on $[0,T]$.
We take the general definition of Gaussian Measure on Banach Space.

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This is inappropriate. –  Graphth Oct 1 '12 at 18:53
You could recall the definition of Gaussian measure. –  Davide Giraudo Oct 1 '12 at 19:15
yeah but how will I show that for all functions f in $ C^{d}$ where $C^{d}$ denotes the dual space of above $C[0,T]$ , we have $f(g)$ which is real valued has a Normal distribution on $R$..From Donsker's theorem its understood but is it possible to proove it via the way I just said?? –  user39646 Oct 1 '12 at 20:26

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