## The Annals of Probability

### Bochner's Theorem in Measurable Dual of Type 2 Banach Space

Yoshiaki Okazaki

#### Abstract

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).

#### Article information

Source
Ann. Probab., Volume 13, Number 3 (1985), 1022-1023.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992925

Digital Object Identifier
doi:10.1214/aop/1176992925

Mathematical Reviews number (MathSciNet)
MR799439

Zentralblatt MATH identifier
0575.60001

JSTOR