Measure-Theoretic Calculus in Abstract Spaces
On the Playground of Infinite-Dimensional Spaces
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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.
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.
Provides an encyclopedic treatment of the fundamental topics in real and functional analysis and measure theory Presents proofs of standard results in the most general abstract settings Discusses several ancillary topics, including probability theory and optimization theory
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Themen in »Measure-Theoretic Calculus in Abstract Spaces«
Measure Theoretic Calculus Infinite-Dimensional Spaces Measure Theory General Integration Theory Lebesgue Dominated Convergence Theorem Banach Space Valued Measure Change of Variable Between Measure Spaces Banach Space of Measures Mode of Convergence Bounded Convergence Theorem Optimization by Vector Space Method Hahn-Banach Theorem Mapping Theorems Sobolev Space