Mathematics and Its Applications

By: Endre Pap, E. Pap

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Hardcover | 30 September 1995

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Hardcover
336 Pages

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23.5 x 16.51 x 2.54

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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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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Set Theory Calculus & Mathematical Analysis Differential Calculus & Equations Mathematical Logic Science Physics Integral Calculus & Equations Business & Management Operational Research

Functional Analysis & Transforms Management & Management Techniques Management Decision Making

Preface
List of Symbols
Introduction	p. 1
General Properties	p. 7
Variations	p. 37
Additive Representations of Set Function	p. 55
Autocontinuity of Set Functions	p. 67
Decompositions of Set Functions	p. 105
Choquet and Sugeno Integrals	p. 139
Integrals Based on Decomposable Measures	p. 192
The Range and Regularity of Null-Additive Set Function	p. 219
Radon-Nikodym Type Theorems and Representation Theorems	p. 231
k-Triangular Set Functions	p. 247
Convergence and Boundedness Theorems on Difference Poset	p. 284
Bibliography	p. 299
Index	p. 313
Table of Contents provided by Blackwell. All Rights Reserved.

Mathematics and Its Applications

At a Glance

Hardcover

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