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Null-Additive Set Functions - E. Pap

Null-Additive Set Functions

(Autor)

Buch | Hardcover
315 Seiten
1995
Springer (Verlag)
978-0-7923-3658-7 (ISBN)
CHF 149,75 inkl. MwSt
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.

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.

Reihe/Serie Mathematics and Its Applications ; 337
Mathematics and Its Applications ; 337
Zusatzinfo XII, 315 p.
Verlagsort Dordrecht
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Logik / Mengenlehre
ISBN-10 0-7923-3658-5 / 0792336585
ISBN-13 978-0-7923-3658-7 / 9780792336587
Zustand Neuware
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