Null-Additive Set Functions

E. Pap

ISBN 10: 0792336585 / ISBN 13: 9780792336587

Published by Springer Netherlands, 1995

About this Item

Zustand: Sehr gut | Seiten: 332 | Sprache: Englisch | Produktart: Bücher | 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.

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Bibliographic Details

• Title: Null-Additive Set Functions
• Publisher: Springer Netherlands
• Publication Date: 1995
• Language: English
• ISBN 10: 0792336585
• ISBN 13: 9780792336587
• Binding: Hardcover
• Condition: Sehr gut
• Seller catalogs:
  • Bücher

About this title

Synopsis

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.