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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Non-Additive Measure and Integral (Hardcover, 1994 ed.)
Loot Price: R6,861
Discovery Miles 68 610
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Non-Additive Measure and Integral (Hardcover, 1994 ed.)
Series: Theory and Decision Library B, 27
Expected to ship within 12 - 17 working days
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Non-Additive Measure and Integral is the first systematic approach
to the subject. Much of the additive theory (convergence theorems,
Lebesgue spaces, representation theorems) is generalized, at least
for submodular measures which are characterized by having a
subadditive integral. The theory is of interest for applications to
economic decision theory (decisions under risk and uncertainty), to
statistics (including belief functions, fuzzy measures) to
cooperative game theory, artificial intelligence, insurance, etc.
Non-Additive Measure and Integral collects the results of scattered
and often isolated approaches to non-additive measures and their
integrals which originate in pure mathematics, potential theory,
statistics, game theory, economic decision theory and other fields
of application. It unifies, simplifies and generalizes known
results and supplements the theory with new results, thus providing
a sound basis for applications and further research in this growing
field of increasing interest. It also contains fundamental results
of sigma-additive and finitely additive measure and integration
theory and sheds new light on additive theory. Non-Additive Measure
and Integral employs distribution functions and quantile functions
as basis tools, thus remaining close to the familiar language of
probability theory. In addition to serving as an important
reference, the book can be used as a mathematics textbook for
graduate courses or seminars, containing many exercises to support
or supplement the text.
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