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On Fréchet differentiability of Lipschitzian functions on spaces with Gaussian measures - MaRDI portal

On Fréchet differentiability of Lipschitzian functions on spaces with Gaussian measures (Q960737)

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scientific article; zbMATH DE number 5493422
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English
On Fréchet differentiability of Lipschitzian functions on spaces with Gaussian measures
scientific article; zbMATH DE number 5493422

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    On Fréchet differentiability of Lipschitzian functions on spaces with Gaussian measures (English)
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    19 January 2009
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    There is a Borel function \(f\) on \({\mathbb R}^{\infty}\) that is Lipschitz with constant~1 along the Cameron-Martin space such that the set of points of Fréchet differentiablity along \(H\) for \(f\) has \(\gamma\)-measure zero, where \(\gamma\) is the standard Gaussian product measure on~\({\mathbb R}^{\infty}\).
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    Fréchet differentiability
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    Lipschitz function
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    Gaussian measure
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    Cameron-Martin space
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