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 weaker requirements characterizes a class of no...
Bewaard in:
| Hoofdauteurs: | , |
|---|---|
| Formaat: | Livre numérique |
| Taal: | Anglais |
| Gepubliceerd in: |
New York, NY :
Springer US
2009.
|
| Editie: | 1st ed. 2009. |
| Reeks: | IFSR International Series in Systems Science and Systems Engineering
25 |
| Onderwerpen: | |
| Online toegang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Opmerking: |
L'impression du document génère 317 p. Description d'après consultation du 20 septembre 2011 Titre provenant de l'écran-titre Numerisation de l'édition de : [s.l.] : Springer science + Business Media. 2009 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Generalized Measure Theory, Texte imprimé, 9781441945761 • Generalized measure theory, Zhenyuan Wang, George J. Klir, New York, Springer, 2009, 1 vol (XV-381 p.), IFSR international series on systems science and engineering, 978-0-387-76851-9 |
| LEADER | 04916nam a22004577a 4500 | ||
|---|---|---|---|
| 001 | 942722 | ||
| 008 | 110106s2009 xxe ||| |||| 00| 0 eng d | ||
| 009 | PPN149048122 | ||
| 020 | |a 9780387768526 | ||
| 041 | 0 | |a eng | |
| 082 | |a 515.42 | ||
| 084 | |a 28-01. 2000 | ||
| 084 | |a 28E05. 2000 | ||
| 084 | |a 28A12. 2000 | ||
| 084 | |a 28B15. 2000 | ||
| 100 | 1 | |a Wang, Zhenyuan, |d 1949- | |
| 245 | 1 | 0 | |a Generalized measure theory |c by Zhenyuan Wang, George J. Klir. |
| 250 | |a 1st ed. 2009. | ||
| 256 | |a Données textuelles | ||
| 260 | |a New York, NY : |b Springer US, |c 2009. | ||
| 490 | 0 | |a IFSR International Series in Systems Science and Systems Engineering |v 25 |x 2698-5497 | |
| 500 | |a L'impression du document génère 317 p. | ||
| 500 | |a Description d'après consultation du 20 septembre 2011 | ||
| 500 | |a Titre provenant de l'écran-titre | ||
| 500 | |a Numerisation de l'édition de : [s.l.] : Springer science + Business Media. 2009 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a 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. | |
| 520 | |a 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 weaker requirements characterizes a class of nonadditive measures. This results in new concepts and methods that allow us to deal with many problems in a more realistic way. For example, it allows us to work with imprecise probabilities. The exposition of generalized measure theory unfolds systematically. It begins 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. About the Authors: Zhenyuan Wang is currently a Professor in the Department of Mathematics of University of Nebraska at Omaha. His research interests have been in the areas of nonadditive measures, nonlinear integrals, probability and statistics, and data mining. He has published one book and many papers in these areas. George J. Klir is currently a Distinguished Professor of Systems Science at Binghamton University (SUNY at Binghamton). He has published 29 books and well over 300 papers in a wide range of areas. His current research interests are primarily in the areas of fuzzy systems, soft computing, and generalized information theory. | ||
| 538 | |a Nécessite un lecteur de fichier PDF | ||
| 650 | |a Intégrales généralisées | ||
| 650 | |a Théorie de la mesure | ||
| 700 | 1 | |a Klir, George J. |4 aut | |
| 776 | 0 | |t Generalized Measure Theory |b Texte imprimé |z 9781441945761 | |
| 776 | 0 | |0 145758214 |t Generalized measure theory |f Zhenyuan Wang, George J. Klir |c New York |n Springer |d 2009 |p 1 vol (XV-381 p.) |s IFSR international series on systems science and engineering |z 978-0-387-76851-9 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-0-387-76852-6 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |q PDF |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-4KGQC7J5-7 |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:74783797X |u https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/978-0-387-76852-6 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:750855487 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-0-387-76852-6 |z Accès INSA CVL | |
| 997 | |0 942722 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||