Countably-Normed Spaces, Their Dual, and the Gaussian Measure
Functional Analysis
2007-05-23 v3
Abstract
Here we present an overview of countably-normed spaces. We discuss the main topologies--weak, strong, and inductive--placed on the dual of a countably-normed space and discuss the sigma-fields generated by these topologies. In particular, we show that under certain conditions the strong and inductive topologies coincide and the sigma-fields generated by the weak, strong, and inductive topologies are equal. With these sigma-fields, we develop a Gaussian measure on the dual of a nuclear space. The purpose in mind is to provide the background material for many of the results used is White Noise Analysis.
Keywords
Cite
@article{arxiv.math/0407200,
title = {Countably-Normed Spaces, Their Dual, and the Gaussian Measure},
author = {Jeremy J. Becnel},
journal= {arXiv preprint arXiv:math/0407200},
year = {2007}
}
Comments
25 pages, 0 figures, Background material for White Noise Analysis