Generalized Measure Theory
This comprehensive text examines the relatively new mathematical area of generalized measure theory. This area expands classical measure theory by abandoning the requirement of additivity and replacing it with various weaker requirements. Each of these we
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International Federation for Systems Research International Series on Systems Science and Engineering Series Editor: George J. Klir State University of New York at Binghamton Editorial Board Gerrit Broekstra Erasmus University, Rotterdam, The Netherlands John L. Casti Santa Fe Institute, New Mexico Brian Gaines University of Calgary, Canada
Ivan M. Havel Charles University, Prague, Czech Republic Klaus Kornwachs Technical University of Cottbus, Germany Franz Pichler University of Linz, Austria
Volume 20
FUZZY RELATIONAL SYSTEMS: Foundations and Principles Radim Be˘lohla´vek
Volume 21
ARCHITECTURE OF SYSTEMS PROBLEMS SOLVING, Second Edition George J. Klir and Doug Elias
Volume 22
ORGANIZATION STRUCTURE: Cybernetic Systems Foundation Yasuhiko Takahara and Mihajlo Mesarovic
Volume 23
CONSTRAINT THEORY: Multidimensional Mathematical Model Management George J. Friedman
Volume 24
FOUNDATIONS AND APPLICATIONS OF MIS: Model Theory Approach Yasuhiko Takahara and Yongmei Liu
Volume 25
GENERALIZED MEASURE THEORY Zhenuyan Wang and George J. Klir
IFSR was established ‘‘to stimulate all activities associated with the scientific study of systems and to coordinate such activities at international level.’’ The aim of this series is to stimulate publication of high-quality monographs and textbooks on various topics of systems science and engineering. This series complements the Federation’s other publications. A Continuation Order Plan is available for this series. A continuation order will bring delivery of each new volume immediately upon publication. Volumes are billed only upon actual shipment. For further information please contact the publisher. Volumes 1–6 were published by Pergamon Press.
GENERALIZED MEASURE THEORY Zhenyuan Wang George J. Klir
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Zhenyuan Wang Department of Mathematics University of Nebraska at Omaha Omaha, NE 68182-0243 U.S.A [email protected]
George J. Klir Thomas J. Watson School of Engineering and Applied Sciences Department of Systems Science and Industrial Engineering Binghamton University Binghamton, NY 13902 U.S.A [email protected]
ISBN: 978-0-387-76851-9 e-ISBN: 978-0-387-76852-6 DOI: 10.1007/978-0-387-76852-6 Library of Congress Control Number: 2008927635 Mathematics Subject Classification (2000): 28-01, 28E-05, 28E-10, 28A-12, 28A-25, 28B-15 # 2009 Springer ScienceþBusiness Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer ScienceþBusiness Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not
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