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A Representation theorem for measures on infinite dimensional spaces Harpain, Franz Peter Edward
Abstract
In this paper we obtain a generalization of the well known Riesz Representation Theorem to the case where the underlying space X is an infinite dimensional product of locally compact, regular and σ-compact topological spaces. In the process we prove that our measures on X correspond to projective limit measures of projective systems of regular Borel measures on the coordinate spaces. An example is given to show that σ-compactness of the coordinate spaces is necessary.
Item Metadata
| Title |
A Representation theorem for measures on infinite dimensional spaces
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
1968
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| Description |
In this paper we obtain a generalization of the well known Riesz Representation Theorem to the case where the underlying space X is an infinite dimensional product of locally compact, regular and σ-compact topological spaces. In the process we prove that our measures on X correspond to projective limit measures of projective systems of regular Borel measures on the coordinate spaces.
An example is given to show that σ-compactness of the coordinate spaces is necessary.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2011-07-22
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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 |
10.14288/1.0302255
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| URI | |
| Degree | |
| Program | |
| 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.