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Null-Additive Set Functions : Water Science and Technology - Endre Pap

Null-Additive Set Functions

Water Science and Technology

By: Endre Pap

Hardcover

Published: 30th September 1995
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RRP $547.99
$502.50

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
List of Symbols
Introductionp. 1
General Propertiesp. 7
Variationsp. 37
Additive Representations of Set Functionp. 55
Autocontinuity of Set Functionsp. 67
Decompositions of Set Functionsp. 105
Choquet and Sugeno Integralsp. 139
Integrals Based on Decomposable Measuresp. 192
The Range and Regularity of Null-Additive Set Functionp. 219
Radon-Nikodym Type Theorems and Representation Theoremsp. 231
k-Triangular Set Functionsp. 247
Convergence and Boundedness Theorems on Difference Posetp. 284
Bibliographyp. 299
Indexp. 313
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792336587
ISBN-10: 0792336585
Series: Mathematics and its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 327
Published: 30th September 1995
Publisher: Kluwer Academic Publishers
Dimensions (cm): 23.4 x 15.6  x 1.9
Weight (kg): 1.43