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Bochner’s theorem in measurable dual of type 2 Banach space. (English) Zbl 0575.60001

Let \(\mu\) be a Radon probability measure on a type 2 Banach space E. The following Bochner’s theorem is proved. For every continuous positive definite function \(\phi\) \((\phi (0)=1)\) on E, there exists a Radon probability measure \(\sigma_{\phi}\) on the measurable dual \(H_ 0(\mu)\) of (E,\(\mu)\) with the characteristic functional \(\phi\) (in some restricted sense).

MSC:

60B05 Probability measures on topological spaces
46B20 Geometry and structure of normed linear spaces
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