Null-Additive Set Functions

1995
ISBN: 978-0-7923-3658-7
Verlag: Springer Netherlands

Buch, Englisch, Band 337, 315 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1430 g

Reihe: Mathematics and Its Applications

This volume presents a unified approach to the mathematical theory of a wide class of non-additive set functions, the so called null-additive set functions, which also includes classical measure theory. It includes such important set functions as capacities, triangular set functions, some fuzzy measures, submeasures, decomposable measures, possibility measures, distorted probabilities, autocontinuous set functions, etc.
The usefulness of the theory is demonstrated by applications in nonlinear differential and difference equations; fractal geometry in the theory of chaos; the approximation of functions in modular spaces by nonlinear singular integral operators; and in the theory of diagonal theorems as a universal method for proving general and fundamental theorems in functional analysis and measure theory.
This book will be of value to researchers and postgraduate students in mathematics, as well as in such diverse fields as knowledge engineering, artificial intelligence, game theory, statistics, economics, sociology and industry.

Zielgruppe

Research

Autoren/Hrsg.

Pap, E.

Fachgebiete

• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik

Inhaltsverzeichnis

Preface. 1. Introduction. 2. Null-additive set functions. 3. Autocontinuity of null-additive set functions. 4. Atoms of null-additive set functions. 5. Choquet and Sugeno integral. 6. Lebesgue decomposition and regularity of null-additive set functions. 7. The range of null-additive set function. 8. k-Triangular set functions. 9. Uniform space valued set functions. 10. Integrals based on decomposable measures. References. Index.