## The Annals of Probability

### Regularite De Fonctions Aleatoires Gaussiennes a Valeurs Vectorielles

X. Fernique

#### Abstract

In this paper, we give a simple condition ensuring that a Gaussian random function $X$ on a metric space $T$ with values in a Lusin topological vector space has a modification with continuous paths. This result extends previous results where $X$ was supposed to be stationary or have stationary increments. As in the stationary case, proof is based on Talagrand's theorem about the majorizing measures which permit us, if $E$ is a separable Banach space, to bound the law of the maximum on $T$ of the norm of $X$ in $E$.

#### Article information

Source
Ann. Probab., Volume 18, Number 4 (1990), 1739-1745.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176990644

Digital Object Identifier
doi:10.1214/aop/1176990644

Mathematical Reviews number (MathSciNet)
MR1071821

Zentralblatt MATH identifier
0718.60037

JSTOR