Gaussian Measures on L sup P Spaces, 1 Less than or Equal to p Less than Infinity,
Abstract
One of the main ideas in the paper is to establish a one to one correspondence between Gaussian measures on L sub p, 1 < or = p < infinity, and Gaussian stochastic processes with sample paths in L sub p. This idea is used to prove a number of interesting results about Gaussian measures on L sub p. Using a recent result of Jain and Kallianpur, a zero-one law for Gaussian measures on Frechet spaces is proved, which is subsequently applied to obtain two other zero-one laws. In the first, it is shown that the smaple paths of a zero-mean measurable Gaussian stochastic process belong to L sub p with probability zero or one; and in the second, it is shown that a certain random series converges uniformly, on any Borel subset of the real line, with probability zero or one. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1971
- Accession Number
- AD0734650
Entities
People
- Belram S. Rajput
Organizations
- University of North Carolina at Chapel Hill