  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.
