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Operator-Valued Measures and Integrals for Cone-Valued Functions [electronic resource] /by Walter Roth.

by Roth, Walter [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Mathematics: 1964Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.Description: online resource.ISBN: 9783540875659.Subject(s): Mathematics | Functional analysis | Mathematics | Measure and Integration | Functional AnalysisDDC classification: 515.42 Online resources: Click here to access online
Contents:
Locally Convex Cones -- Measures and Integrals. The General Theory -- Measures on Locally Compact Spaces.
In: Springer eBooksSummary: 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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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.

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