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On Zabczyk & Da Prato book about infinite dimensional SDEs they introduce the idea of Gaussian measures in infinite dimensional Banach spaces. They do so by means of Fernique theorem. In the White Noise framework, we also deal with Gaussian measures defined on infinite dimensional spaces, in the more classical case we work with the space of tempered distributions $S(\mathbb R)$$S'(\mathbb R)$, and they are introducesintroduced by means of the Bochner-Minlos theorem.

My question is, can we "exchange" those approaches, namely can we use Bochner-Minlos (or some modification) to define a Gaussian measure on Banach space? and is there another way to introduce Gaussian measures on white noise spaces without using B-M. ?

Any idea, suggestion or comment will be greatly appreciated.

On Zabczyk & Da Prato book about infinite dimensional SDEs they introduce the idea of Gaussian measures in infinite dimensional Banach spaces. They do so by means of Fernique theorem. In the White Noise framework, we also deal with Gaussian measures defined on infinite dimensional spaces, in the more classical case we work with the space of tempered distributions $S(\mathbb R)$, and they are introduces by means of the Bochner-Minlos theorem.

My question is, can we "exchange" those approaches, namely can we use Bochner-Minlos (or some modification) to define a Gaussian measure on Banach space? and is there another way to introduce Gaussian measures on white noise spaces without using B-M. ?

Any idea, suggestion or comment will be greatly appreciated.

On Zabczyk & Da Prato book about infinite dimensional SDEs they introduce the idea of Gaussian measures in infinite dimensional Banach spaces. They do so by means of Fernique theorem. In the White Noise framework, we also deal with Gaussian measures defined on infinite dimensional spaces, in the more classical case we work with the space of tempered distributions $S'(\mathbb R)$, and they are introduced by means of the Bochner-Minlos theorem.

My question is, can we "exchange" those approaches, namely can we use Bochner-Minlos (or some modification) to define a Gaussian measure on Banach space? and is there another way to introduce Gaussian measures on white noise spaces without using B-M. ?

Any idea, suggestion or comment will be greatly appreciated.

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Gaussian measures on infinite dimensional spaces

On Zabczyk & Da Prato book about infinite dimensional SDEs they introduce the idea of Gaussian measures in infinite dimensional Banach spaces. They do so by means of Fernique theorem. In the White Noise framework, we also deal with Gaussian measures defined on infinite dimensional spaces, in the more classical case we work with the space of tempered distributions $S(\mathbb R)$, and they are introduces by means of the Bochner-Minlos theorem.

My question is, can we "exchange" those approaches, namely can we use Bochner-Minlos (or some modification) to define a Gaussian measure on Banach space? and is there another way to introduce Gaussian measures on white noise spaces without using B-M. ?

Any idea, suggestion or comment will be greatly appreciated.