Operator-Valued Measures and Integrals for Cone-Valued Functions
Roth, Walter.
Operator-Valued Measures and Integrals for Cone-Valued Functions [electronic resource] / by Walter Roth. - X, 356 p. online resource. - Lecture Notes in Mathematics, 1964 0075-8434 ; . - Lecture Notes in Mathematics, 1964 .
Locally Convex Cones -- Measures and Integrals. The General Theory -- Measures on Locally Compact Spaces.
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.
9783540875659
10.1007/978-3-540-87565-9 doi
Mathematics.
Functional analysis.
Measure and Integration.
Functional Analysis.
QA312-312.5
515.42
Operator-Valued Measures and Integrals for Cone-Valued Functions [electronic resource] / by Walter Roth. - X, 356 p. online resource. - Lecture Notes in Mathematics, 1964 0075-8434 ; . - Lecture Notes in Mathematics, 1964 .
Locally Convex Cones -- Measures and Integrals. The General Theory -- Measures on Locally Compact Spaces.
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.
9783540875659
10.1007/978-3-540-87565-9 doi
Mathematics.
Functional analysis.
Measure and Integration.
Functional Analysis.
QA312-312.5
515.42