
Null-Additive Set Functions
E. Pap(Author)
Springer (Publisher)
Published on 15. December 2010
Book
Paperback/Softback
XII, 315 pages
978-90-481-4602-4 (ISBN)
Description
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.
Audience: 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.
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.
Audience: 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.
More details
Series
Edition
1st ed. Softcover of orig. ed. 1995
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Illustrations
XII, 315 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 18 mm
Weight
499 gr
ISBN-13
978-90-481-4602-4 (9789048146024)
Schweitzer Classification
Other editions
Additional editions

E. Pap
Null-Additive Set Functions
Book
09/1995
Kluwer Academic Publishers
€106.99
Shipment within 15-20 days
Content
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.