Operator-Valued Measures and Integrals for Cone-Valued Functions
Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions. Different approaches are applied in each of these cases using different techniques. The order structure of the (extended) real number system is used for real-valued functions and measures, w...
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| Format: | Electronic |
| Language: | English |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg,
2009.
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| Series: | Lecture Notes in Mathematics,
1964 |
| Subjects: | |
| Online Access: | https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-87565-9 |
| Summary: | Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions. Different approaches are applied in each of these cases using different techniques. The order structure of the (extended) real number system is used for real-valued functions and measures, whereas suprema and infima are replaced with topological limits in the vector-valued case. A novel approach employing more general structures, locally convex cones, which are natural generalizations of locally convex vector spaces, is introduced here. This setting allows developing a general theory of integration which simultaneously deals with all of the above-mentioned cases. |
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| Physical Description: | online resource. |
| ISBN: | 9783540875659 |
| ISSN: | 0075-8434 ; |