Pan Z. Measure-Theoretic Calculus in Abstract Spaces: On the Playground of Infinite-Dimensional Spaces

Birkhäuser, 2024. — 950 p. — ISBN 3031219112.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.Preface.
Introduction.
Set Theory.
Topological Spaces.
Metric Spaces.
Compact and Locally Compact Spaces.
Vector Spaces.
Banach Spaces.
Global Theory of Optimization.
Differentiation in Banach Spaces.
Local Theory of Optimization.
General Measure and Integration.
Differentiation and Integration.
Hilbert Spaces.
Probability Theory.
A Elements in Calculus.
Bibliography.
Index.True PDF