Generalized Measure Theory

  • Zhenyuan Wang
  • George J. Klir

Part of the IFSR International Series on Systems Science and Engineering book series (IFSR, volume 25)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Zhenyuan Wang, George J. Klir
    Pages 1-8
  3. Zhenyuan Wang, George J. Klir
    Pages 9-60
  4. Zhenyuan Wang, George J. Klir
    Pages 61-72
  5. Zhenyuan Wang, George J. Klir
    Pages 73-103
  6. Zhenyuan Wang, George J. Klir
    Pages 111-132
  7. Zhenyuan Wang, George J. Klir
    Pages 133-150
  8. Zhenyuan Wang, George J. Klir
    Pages 151-165
  9. Zhenyuan Wang, George J. Klir
    Pages 167-178
  10. Zhenyuan Wang, George J. Klir
    Pages 179-211
  11. Zhenyuan Wang, George J. Klir
    Pages 213-223
  12. Zhenyuan Wang, George J. Klir
    Pages 225-246
  13. Zhenyuan Wang, George J. Klir
    Pages 247-274
  14. Zhenyuan Wang, George J. Klir
    Pages 275-284
  15. Zhenyuan Wang, George J. Klir
    Pages 285-302
  16. Zhenyuan Wang, George J. Klir
    Pages 303-342
  17. Back Matter
    Pages 343-381

About this book

Introduction

This comprehensive text examines the relatively new mathematical area of generalized measure theory. This area expands classical measure theory by abandoning the requirement of additivity and replacing it with various weaker requirements. Each of these weaker requirements characterizes a class of nonadditive measures. This results in new concepts and methods that allow us to deal with many problems in a more realistic way. For example, it allows us to work with imprecise probabilities.

The exposition of generalized measure theory unfolds systematically. It begins with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous examples, culminating in a final chapter on applications of generalized measure theory.

Some key features of the book include: many exercises at the end of each chapter along with relevant historical and bibliographical notes, an extensive bibliography, and name and subject indices. The work is suitable for a classroom setting at the graduate level in courses or seminars in applied mathematics, computer science, engineering, and some areas of science. A sound background in mathematical analysis is required. Since the book contains many original results by the authors, it will also appeal to researchers working in the emerging area of generalized measure theory.

About the Authors:

Zhenyuan Wang is currently a Professor in the Department of Mathematics of University of Nebraska at Omaha. His research interests have been in the areas of nonadditive measures, nonlinear integrals, probability and statistics, and data mining. He has published one book and many papers in these areas.

George J. Klir is currently a Distinguished Professor of Systems Science at Binghamton University (SUNY at Binghamton). He has published 29 books and well over 300 papers in a wide range of areas. His current research interests are primarily in the areas of fuzzy systems, soft computing, and generalized information theory.

Keywords

choquet integral integral integration mathematical analysis measure measure theory

Authors and affiliations

  • Zhenyuan Wang
    • 1
  • George J. Klir
    • 2
  1. 1.Department of MathematicsUniversity of Nebraska at OmahaOmahaU.S.A.
  2. 2.Thomas J. Watson School of Engineering, Department of Systems Science &Binghamton UniversityBinghamtonU.S.A.

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-76852-6
  • Copyright Information Springer-Verlag US 2009
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-76851-9
  • Online ISBN 978-0-387-76852-6
  • Series Print ISSN 1574-0463
  • About this book