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Integral, Measure, and Ordering : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - Beloslav Riecan

Integral, Measure, and Ordering


Hardcover Published: 31st July 1997
ISBN: 9780792345664
Number Of Pages: 378

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The present book is a monograph including some recent results of mea­ sure and integration theory. It concerns three main ideas. The first idea deals with some ordering structures such as Riesz spaces and lattice or­ dered groups, and their relation to measure and integration theory. The second is the idea of fuzzy sets, quite new in general, and in measure theory particularly. The third area concerns some models of quantum mechanical systems. We study mainly models based on fuzzy set theory. Some recent results are systematically presented along with our suggestions for further development. The first chapter has an introductory character, where we present basic definitions and notations. Simultaneously, this chapter can be regarded as an elementary introduction to fuzzy set theory. Chapter 2 contains an original approach to the convergence of sequences of measurable functions. While the notion of a null set can be determined uniquely, the notion of a set of "small" measure has a fuzzy character. It is interesting that the notion of fuzzy set and the notion of a set of small measure (described mathematically by so-called small systems) were introduced independently at almost the same time. Although the axiomatic systems in both theories mentioned are quite different, we show that the notion of a small system can be considered from the point of view of fuzzy sets.

Sets and fuzzy setsp. 1
Null sets and small systemsp. 15
Measures on ordered spacesp. 34
Subadditive measuresp. 59
The Kurzweil integral in ordered spacesp. 70
Quantum logicsp. 103
Fuzzy-quantum spacesp. 127
Fuzzy quantum logicsp. 142
Probability on MV algebrasp. 183
The entropy of fuzzy dynamical systemsp. 213
Measurability and integrability of multifunctionsp. 252
D-posetsp. 278
Notes on order convergence and order topologyp. 312
Referencesp. 326
Indexp. 374
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792345664
ISBN-10: 0792345665
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 378
Published: 31st July 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.77 x 17.15  x 2.54
Weight (kg): 0.79