Generalized Measure Theory

• Main Authors: Wang, Zhenyuan. (Author), Klir, George J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Boston, MA : Springer US, 2009.
• Series: IFSR International Series on Systems Science and Engineering, 25
• Subjects: Mathematics.; Systems theory.; Logic, Symbolic and mathematical.; Measure and Integration.; Mathematical Logic and Foundations.; Systems Theory, Control.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-76852-6

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 no...

Table of Contents:

• Preface
• Introduction
• Preliminaries
• Basic Ideas of Generalized Measure Theory
• Special Area of Generalized Measure Theory
• Extensions
• Structural Characteristics
• Measurable Functions on Monotone Measure Space
• Integration
• Sugeno Integrals
• Pan-Intergrals
• Choquet Integral
• Upper and Lower Integrations
• Constructing Generalized Measures
• Fuzzification in Generalized Measure Theory
• Applications of Generalized Measure Theory
• Bibliography
• Appendix A. Glossary of Key Concepts
• Appendix B. Glossary of Symbols
• Name Index
• Subject Index.