IFSR International Series in Systems Science and Systems Engineering

Generalized Measure Theory

Authors: Wang, Zhenyuan, Klir, George

  • Most up-to-date textbook in the field, covering recent applications
  • Numerous examples illustrate the theory, while exercises at the end of the chapter provide practice to the student
  • Useful to an interdisciplinary cadre of mathematicians, engineers, computer scientists and specialists working in decision-making
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Hardcover $79.95
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Softcover $79.95
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About this Textbook

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.

Reviews

From the reviews:

“The monograph contains many original results of the authors and provides an excellent introduction to the emerging field of generalized measure theory. The presentation of the large material is given with didactical skill, numerous examples serve for motivation and illustration of results. … easy to read by everyone with a solid background in mathematical analysis, and on this basis in particular for students in mathematics and engineering at the graduate level. … this book can serve as a starting point for research in this area.” (Jan Stankiewicz, Zentralblatt MATH, Vol. 1184, 2010)

Table of contents (15 chapters)

  • Introduction

    Wang, Zhenyuan (et al.)

    Pages 1-8

  • Applications of Generalized Measure Theory

    Wang, Zhenyuan (et al.)

    Pages 1-40

  • Preliminaries

    Wang, Zhenyuan (et al.)

    Pages 9-60

  • Basic Ideas of Generalized Measure Theory

    Wang, Zhenyuan (et al.)

    Pages 61-72

  • Special Areas of Generalized Measure Theory

    Wang, Zhenyuan (et al.)

    Pages 73-103

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-0-387-76852-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-0-387-76851-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-1-4419-4576-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Generalized Measure Theory
Authors
Series Title
IFSR International Series in Systems Science and Systems Engineering
Series Volume
25
Copyright
2009
Publisher
Springer US
Copyright Holder
Springer-Verlag US
eBook ISBN
978-0-387-76852-6
DOI
10.1007/978-0-387-76852-6
Hardcover ISBN
978-0-387-76851-9
Softcover ISBN
978-1-4419-4576-1
Series ISSN
1574-0463
Edition Number
1
Number of Pages
XVI, 384
Number of Illustrations and Tables
25 b/w illustrations
Topics