In this paper we present a theory of cylinder measures from the viewpoint of inverse systems of measure spaces. Specifically, we consider the problem of finding limits for the inverse system of measure spaces determined by a cylinder measure μ over a vector space X.
For any subspace Ω of the algebraic dual X* such that (X,Ω) is a dual pair, we establish conditions on μ which ensure the existence of a limit measure on Ω .
For any regular topology G on Ω, finer than the topology of pointwise convergence, we give a necessary and sufficient condition on μ for it to have a limit measure on Ω Radon with respect to G
We introduce the concept of a weighted system in a locally convex space. When X is a Hausdorff, locally convex space, and Ω is the topological dual of X , we use this concept in deriving further conditions under which μ will have a limit measure on Ω Radon with respect to G.
We apply our theory to the study of cylinder measures over Hilbertian spaces and ℓ(ρ)-spaces, obtaining significant extensions and clarifications of many previously known results. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/34276 |
| Date | January 1971 |
| Creators | Millington, Hugh Gladstone Roy |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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