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 $H'$.
Publié le : 1981-08-14
Classification:
Bochner's theorem,
measurable linear functional,
Gaussian measure,
random linear functional,
cotype 2,
2-summing operator,
28A40,
60B05
@article{1176994372,
author = {Okazaki, Yoshiaki},
title = {Bochner's Theorem on Measurable Linear Functionals of a Gaussian Measure},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 663-664},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994372}
}
Okazaki, Yoshiaki. Bochner's Theorem on Measurable Linear Functionals of a Gaussian Measure. Ann. Probab., Tome 9 (1981) no. 6, pp. 663-664. http://gdmltest.u-ga.fr/item/1176994372/