Open Access
August, 1985 Bochner's Theorem in Measurable Dual of Type 2 Banach Space
Yoshiaki Okazaki
Ann. Probab. 13(3): 1022-1023 (August, 1985). DOI: 10.1214/aop/1176992925


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).


Download Citation

Yoshiaki Okazaki. "Bochner's Theorem in Measurable Dual of Type 2 Banach Space." Ann. Probab. 13 (3) 1022 - 1023, August, 1985.


Published: August, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0575.60001
MathSciNet: MR799439
Digital Object Identifier: 10.1214/aop/1176992925

Primary: 28C20
Secondary: 60B11

Keywords: Bochner's theorem , measurable dual , pre-Gaussian measure , type 2 Banach space

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 3 • August, 1985
Back to Top