Operator-Valued Measures and Integrals for Cone-Valued Functions: 1964 (Lecture Notes in Mathematics, 1964) - Softcover

Roth, Walter

Softcover

ISBN 10: 3540875646 ISBN 13: 9783540875642

Publisher: Springer, 2009

Synopsis

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.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2009
• Language: English
• ISBN 10: 3540875646
• ISBN 13: 9783540875642
• Binding: Paperback
• Number of pages: 366