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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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Operator valued measures and integrals for cone valued functions, Walter Roth
- Language
- Released
- 2009
Payment methods
- Title
- Operator valued measures and integrals for cone valued functions
- Language
- English
- Authors
- Walter Roth
- Publisher
- Springer
- Publisher
- 2009
- Format
- Paperback
- ISBN10
- 3540875646
- ISBN13
- 9783540875642
- Category
- Mathematics
- Description
- 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.