Generalized Measure Theory / Edition 1

Generalized Measure Theory / Edition 1

by Zhenyuan Wang, George Klir
     
 

ISBN-10: 0387768513

ISBN-13: 9780387768519

Pub. Date: 10/10/2008

Publisher: Springer US

Generalized Measure Theory examines the relatively new mathematical area of generalized measure theory. The exposition unfolds systematically, beginning with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves several

…  See more details below

Overview

Generalized Measure Theory examines the relatively new mathematical area of generalized measure theory. The exposition unfolds systematically, beginning with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous examples, culminating in a final chapter on applications of generalized measure theory.

Some key features of the book include: many exercises at the end of each chapter along with relevant historical and bibliographical notes, an extensive bibliography, and name and subject indices. The work is suitable for a classroom setting at the graduate level in courses or seminars in applied mathematics, computer science, engineering, and some areas of science. A sound background in mathematical analysis is required. Since the book contains many original results by the authors, it will also appeal to researchers working in the emerging area of generalized measure theory.

Read More

Product Details

ISBN-13:
9780387768519
Publisher:
Springer US
Publication date:
10/10/2008
Series:
IFSR International Series on Systems Science and Engineering, #25
Edition description:
2009
Pages:
384
Product dimensions:
6.30(w) x 9.30(h) x 0.90(d)
Age Range:
3 Months

Table of Contents

Preliminaries.- Basic Ideas of Generalized Measure Theory.- Special Areas of Generalized Measure Theory.- Extensions.- Structural Characteristics for Set Functions.- Measurable Functions on Monotone Measure Spaces.- Integration.- Sugeno Integrals.- Pan-Integrals.- Choquet Integrals.- Upper and Lower Integrals.- Constructing General Measures.- Fuzzification of Generalized Measures and the Choquet Integral.- Applications of Generalized Measure Theory.

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >