Generalized Measure Theory

• Main Authors: Wang, Zhenyuan (Author), Klir, George J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Springer US, 2009.
• Series: IFSR International Series on Systems Science and Engineering, 25
• Subjects: Mathematics.; Measure theory.; System theory.; Mathematical logic.; Measure and Integration.; Mathematical Logic and Foundations.; Systems Theory, Control.

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:

• Preliminaries
• Basic Ideas of Generalized Measure Theory
• Special Areas of Generalized Measure Theory
• Extensions
• Structural Characteristics for Set Functions
• Measurable Functions on Monotone Measure Spaces
• Integration
• Sugeno Integrals
• Pan-Integrals
• Choquet Integrals
• Upper and Lower Integrals
• Constructing General Measures
• Fuzzification of Generalized Measures and the Choquet Integral
• Applications of Generalized Measure Theory.