Leseprobe
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Measure-Theoretic Calculus in Abstract Spaces
Zigang Pan
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Springer International Publishing 
Naturwissenschaften, Medizin, Informatik, Technik / Analysis
Beschreibung
This monograph provides a rigorous, encyclopedic treatment of the fundamental topics in real analysis, functional analysis, and measure theory. The result of many years of the author’s careful and extensive work, this text synthesizes and builds upon the existing literature in an effort to develop and solidify the theory of measure-theoretic calculus in abstract spaces. Standard results and proofs are illustrated in general abstract settings under rigorous treatment, and numerous ancillary topics are also covered in detail, such as functional analytic treatment of optimization, probability theory, and the theory of Sobolev spaces. Applied mathematicians and researchers working in control theory, operations research, economics, optimization theory, and many other areas will find this text to be a comprehensive and invaluable resource. It can also serve as an analysis textbook for graduate-level students.
Kundenbewertungen
Bounded Convergence Theorem, Infinite-Dimensional Spaces, Mode of Convergence, Sobolev Space, Banach Space of Measures, Hahn-Banach Theorem, Optimization by Vector Space Method, Banach Space Valued Measure, Measure Theoretic Calculus, General Integration Theory, Change of Variable Between Measure Spaces, Mapping Theorems, Lebesgue Dominated Convergence Theorem, Measure Theory