Operator-Valued Measures and Integrals for Cone-Valued Functions

  • Walter Roth

Part of the Lecture Notes in Mathematics book series (LNM, volume 1964)

Table of contents

  1. Front Matter
    Pages i-x
  2. Pages 1-7
  3. Pages 9-117
  4. Back Matter
    Pages 341-362

About this book

Introduction

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.

Keywords

Compact space Cone-valued functions DEX Integral representation Locally convex cones Natural Vector space Vector-valued measures boundary element method integral integration integration theory real number system techniques

Authors and affiliations

  • Walter Roth
    • 1
  1. 1.Department of MathematicsUniversity of Brunei DarussalamGadongBrunei Darussalam

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-87565-9
  • Copyright Information Springer Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-87564-2
  • Online ISBN 978-3-540-87565-9
  • Series Print ISSN 0075-8434
  • About this book