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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
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Integral, Measure, and Ordering (Paperback, Softcover reprint of hardcover 1st ed. 1997)
Loot Price: R5,751
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Integral, Measure, and Ordering (Paperback, Softcover reprint of hardcover 1st ed. 1997)
Series: Mathematics and Its Applications, 411
Expected to ship within 10 - 15 working days
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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."
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