A Riesz representation theorem for cone-valued functions
We consider Borel measures on a locally compact Hausdorff space whose values are linear functionals on a locally convex cone. We define integrals for cone-valued functions and verify that continuous linear functionals on certain spaces of continuous cone-valued functions endowed with an inductive li...
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337599000160 |
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| _version_ | 1832564666309541888 |
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| author | Walter Roth |
| author_facet | Walter Roth |
| author_sort | Walter Roth |
| collection | DOAJ |
| description | We consider Borel measures on a locally compact Hausdorff space
whose values are linear functionals on a locally convex cone. We define integrals for cone-valued functions and verify that continuous linear functionals on certain spaces of continuous cone-valued functions endowed with an inductive limit topology may be represented by such integrals. |
| format | Article |
| id | doaj-art-1b577216f6d14f74ac2a2a4ad39fd982 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1b577216f6d14f74ac2a2a4ad39fd9822025-02-03T01:10:24ZengWileyAbstract and Applied Analysis1085-33751687-04091999-01-014420922910.1155/S1085337599000160A Riesz representation theorem for cone-valued functionsWalter Roth0Department of Mathematics, Universiti Brunei Darussalam, Gadong BE 1410, Brunei DarussalamWe consider Borel measures on a locally compact Hausdorff space whose values are linear functionals on a locally convex cone. We define integrals for cone-valued functions and verify that continuous linear functionals on certain spaces of continuous cone-valued functions endowed with an inductive limit topology may be represented by such integrals.http://dx.doi.org/10.1155/S1085337599000160 |
| spellingShingle | Walter Roth A Riesz representation theorem for cone-valued functions Abstract and Applied Analysis |
| title | A Riesz representation theorem for cone-valued functions |
| title_full | A Riesz representation theorem for cone-valued functions |
| title_fullStr | A Riesz representation theorem for cone-valued functions |
| title_full_unstemmed | A Riesz representation theorem for cone-valued functions |
| title_short | A Riesz representation theorem for cone-valued functions |
| title_sort | riesz representation theorem for cone valued functions |
| url | http://dx.doi.org/10.1155/S1085337599000160 |
| work_keys_str_mv | AT walterroth arieszrepresentationtheoremforconevaluedfunctions AT walterroth rieszrepresentationtheoremforconevaluedfunctions |