## The Annals of Probability

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

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

#### 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**

links.jstor.org

**Subjects**

Primary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]

Secondary: 60B11: Probability theory on linear topological spaces [See also 28C20]

**Keywords**

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

#### Citation

Okazaki, Yoshiaki. Bochner's Theorem in Measurable Dual of Type 2 Banach Space. Ann. Probab. 13 (1985), no. 3, 1022--1023. doi:10.1214/aop/1176992925. https://projecteuclid.org/euclid.aop/1176992925