Operator-Valued Measures and Integrals for Cone-Valued Functions [electronic resource] / by Walter Roth.
Tipo de material:
TextoSeries Lecture Notes in Mathematics, 1964Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009Descripción: online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783540875659Trabajos contenidos: SpringerLink (Online service)Tema(s): Mathematics | Functional analysis | Mathematics | Measure and Integration | Functional AnalysisFormatos físicos adicionales: Sin títuloClasificación CDD: 515.42 Clasificación LoC:QA312-312.5Recursos en línea: de clik aquí para ver el libro electrónico 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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