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Generalized Measure Theory

Springer US,
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This 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 associated integration theory.

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Titel: Generalized Measure Theory
Autoren/Herausgeber: Zhenyuan Wang, George Klir
Aus der Reihe: Ifsr International Series on Systems Science and Engineering
Ausgabe: 2009

ISBN/EAN: 9780387768519

Seitenzahl: 384
Format: 23,5 x 15,5 cm
Produktform: Hardcover/Gebunden
Gewicht: 760 g
Sprache: Englisch

In 1992 we published a book entitled Fuzzy Measure Theory (Plenum Press, New York), in which the term ‘‘fuzzy measure’’ was used for set functions obtained by replacing the additivity requirement of classical measures with weaker requirements of monotonicity with respect to set inclusion and con- nuity. That is, the book dealt with nonnegative set functions that were mo- tone, vanished at the empty set, and possessed appropriate continuity properties when defined on infinite sets. It seems that Fuzzy Measure Theory was the only book available on the market at that time devoted to this emerging new mathematical theory. Some ten years after its publication we began to see that the subject had expanded so much that a second edition of the book, or even a new book on the subject, was needed. We eventually decided to write a new book because the new material we wished to include was too extensive for—and far beyond the usual scope—of a second edition. More importantly, we felt that some fundamental changes regarding this topic’s scope and terminology would be desirable and timely.

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