Overview
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.
Full Product Details
Author: Walter Roth
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: 2009 ed.
Volume: 1964
Dimensions:
Width: 15.50cm
, Height: 1.90cm
, Length: 23.50cm
Weight: 0.569kg
ISBN: 9783540875642
ISBN 10: 3540875646
Pages: 356
Publication Date: 05 February 2009
Audience:
Professional and scholarly
,
College/higher education
,
Professional & Vocational
,
Postgraduate, Research & Scholarly
Format: Paperback
Publisher's Status: Active
Availability: In Print
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.
Reviews
From the reviews: The aim of the present book is to use the theory of locally convex cones for developing a very general and unified theory of integration for extended real-valued, vector-valued, operator-valued and cone-valued countably additive measures and functions. ! Providing a very general and nontrivial approach to integration theory, the book is of interest for researchers in functional analysis, abstract integration theory and its applications to integral representations of linear operators. It can be used also for advanced post-graduate courses in functional analysis. (S. CobzaAu, Studia Universitatis BabeAu-Bolyai. Mathematica, Vol. LIV (3), September, 2009)
From the reviews: The aim of the present book is to use the theory of locally convex cones for developing a very general and unified theory of integration for extended real-valued, vector-valued, operator-valued and cone-valued countably additive measures and functions. ! Providing a very general and nontrivial approach to integration theory, the book is of interest for researchers in functional analysis, abstract integration theory and its applications to integral representations of linear operators. It can be used also for advanced post-graduate courses in functional analysis. (S. Cobzas, Studia Universitatis Babes-Bolyai. Mathematica, Vol. LIV (3), September, 2009) This is an interesting book which firstly presents an extension of the theory of locally convex topological vector spaces ! . Each chapter finishes with notes and remarks. The book is well written and contains many new results. It is well placed for graduated courses and research work. (Miguel A. Jimenez, Zentralblatt MATH, Vol. 1187, 2010)
From the reviews: The aim of the present book is to use the theory of locally convex cones for developing a very general and unified theory of integration for extended real-valued, vector-valued, operator-valued and cone-valued countably additive measures and functions. ! Providing a very general and nontrivial approach to integration theory, the book is of interest for researchers in functional analysis, abstract integration theory and its applications to integral representations of linear operators. It can be used also for advanced post-graduate courses in functional analysis. (S. Cobzas, Studia Universitatis Babes-Bolyai. Mathematica, Vol. LIV (3), September, 2009)
