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

Por: Tipo de material: TextoTextoSeries Lecture Notes in Mathematics ; 1964 | Lecture Notes in Mathematics ; 1964Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009Descripción: online resourceTipo de contenido:
  • text
Tipo de medio:
  • computer
Tipo de soporte:
  • online resource
ISBN:
  • 9783540875659
Trabajos contenidos:
  • SpringerLink (Online service)
Tema(s): Formatos físicos adicionales: Sin títuloClasificación CDD:
  • 515.42 23
Clasificación LoC:
  • QA312-312.5
Recursos en línea:
Contenidos:
Springer eBooksResumen: 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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