Countably-Normed Spaces, Their Dual, and the Gaussian Measure

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dc.creatorBecnel, Jeremy J.
dc.date2004-07-12
dc.date2005-08-24
dc.date.accessioned2026-07-07T05:10:13Z
dc.date.available2026-07-07T05:10:13Z
dc.descriptionHere 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.
dc.description25 pages, 0 figures, Background material for White Noise Analysis
dc.identifierhttps://arxiv.org/abs/math/0407200
dc.identifierhttp://arxiv.org/abs/math/0407200
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71861
dc.subjectFunctional Analysis
dc.subject46A11
dc.titleCountably-Normed Spaces, Their Dual, and the Gaussian Measure
dc.typetext

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