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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.
Geometric aspects of functional analysis: Israel seminar 2004-2005 Автор: Milman V., Schechtman G. (eds.) Год: 2007 |
Geometric Aspects of Functional Analysis Автор: Milman V.D. Год: 2007 |
Convexity Автор: H. G. Eggleston Год: 2009 |
Convex Functional Analysis Автор: Andrew J. Kurdila Год: 2005 |
Convex Functional Analysis Автор: Kurdila A. J., Zabarankin M. Год: 2005 |
Dual Cone and Polar Cone Год: 2011 |