## The Annals of Probability

### Bochner's Theorem on Measurable Linear Functionals of a Gaussian Measure

Yoshiaki Okazaki

#### Abstract

Bochner's theorem formulated by Xia Dao-Xing is established for an abstract Wiener space. Let $(\iota, H, E)$ be an abstract Wiener space. Then for every continuous cylinder set measure $\nu$ on $E'$, the image $\iota'(\nu)$ is a Radon measure on $H'$.

#### Article information

Source
Ann. Probab., Volume 9, Number 4 (1981), 663-664.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176994372

Digital Object Identifier
doi:10.1214/aop/1176994372

Mathematical Reviews number (MathSciNet)
MR624693

Zentralblatt MATH identifier
0458.28014

JSTOR

Subjects
Primary: 28A40
Secondary: 60B05: Probability measures on topological spaces

#### Citation

Okazaki, Yoshiaki. Bochner's Theorem on Measurable Linear Functionals of a Gaussian Measure. Ann. Probab. 9 (1981), no. 4, 663--664. doi:10.1214/aop/1176994372. https://projecteuclid.org/euclid.aop/1176994372