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Cylinder measures over vector spaces Millington, Hugh Gladstone Roy
Abstract
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.
Item Metadata
Title |
Cylinder measures over vector spaces
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1971
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Description |
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.
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Language |
eng
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Date Available |
2011-05-04
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Provider |
Vancouver : University of British Columbia Library
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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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DOI |
10.14288/1.0080478
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Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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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.