Spaces of complex functions and vector measures in incomplete spaces
It is known that the space L1(μ) of complex functions which are integrable with respect to a vector measure μ taking values in a (not neessarily complete) locally convex space is not an ideal, in general. We discuss several natural properties which L1(μ) may or may not possess and consider various i...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2004/413765 |
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| _version_ | 1832565253643173888 |
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| author | Werner Riker Martin Väth |
| author_facet | Werner Riker Martin Väth |
| author_sort | Werner Riker |
| collection | DOAJ |
| description | It is known that the space L1(μ) of complex functions which are integrable with respect to a vector measure μ taking values in a (not neessarily complete) locally convex space is not an ideal, in general. We discuss several natural properties which L1(μ) may or may not possess and consider various implications between these properties. For a particular class of properties, whether or not there exists a partiular space of the form L1(μ) having these properties, is shown to be equivalent to the existence of any space of complex functions on C having these same properties. |
| format | Article |
| id | doaj-art-ae54d7bc1a414721a2a2fb58c3dc830d |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-ae54d7bc1a414721a2a2fb58c3dc830d2025-02-03T01:08:54ZengWileyJournal of Function Spaces and Applications0972-68022004-01-012111610.1155/2004/413765Spaces of complex functions and vector measures in incomplete spacesWerner Riker0Martin Väth1Math.-Geogr. Fakultät, Katholische Universitat Eichstätt-Ingolstadt, D-85071 Eichstätt, GermanyUniversity of Würzburg, Department of Mathematics, Am Hubland, D-97074 Würzburg, GermanyIt is known that the space L1(μ) of complex functions which are integrable with respect to a vector measure μ taking values in a (not neessarily complete) locally convex space is not an ideal, in general. We discuss several natural properties which L1(μ) may or may not possess and consider various implications between these properties. For a particular class of properties, whether or not there exists a partiular space of the form L1(μ) having these properties, is shown to be equivalent to the existence of any space of complex functions on C having these same properties.http://dx.doi.org/10.1155/2004/413765 |
| spellingShingle | Werner Riker Martin Väth Spaces of complex functions and vector measures in incomplete spaces Journal of Function Spaces and Applications |
| title | Spaces of complex functions and vector measures in incomplete spaces |
| title_full | Spaces of complex functions and vector measures in incomplete spaces |
| title_fullStr | Spaces of complex functions and vector measures in incomplete spaces |
| title_full_unstemmed | Spaces of complex functions and vector measures in incomplete spaces |
| title_short | Spaces of complex functions and vector measures in incomplete spaces |
| title_sort | spaces of complex functions and vector measures in incomplete spaces |
| url | http://dx.doi.org/10.1155/2004/413765 |
| work_keys_str_mv | AT wernerriker spacesofcomplexfunctionsandvectormeasuresinincompletespaces AT martinvath spacesofcomplexfunctionsandvectormeasuresinincompletespaces |