Operator-Valued Measures and Integrals for Cone-Valued Functions [electronic resource] /
Roth, Walter.author.
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.
Bibliographic Level Mode of Issuance: Monograph
Includes bibliographical references (p. 345-352) and index.
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.
Measure theory.
Functional analysis.
Measure and Integration.
Functional Analysis.
Lecture notes in mathematics