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About this book :-
Measure and Integration written by
Dietmar A. Salamon.
This book is based on notes for the lecture course “Measure and Integration” held at ETH Z¨urich in the spring semester 2014. Prerequisites are the first year courses on Analysis and Linear Algebra, including the Riemann integral, as well as some basic knowledge of metric and topological spaces.
The course material is based in large parts on Chapters 1-8 of the textbook “Real and Complex Analysis” by Walter Rudin. In addition to Rudin’s book the lecture notes by Urs Lang, the five volumes on measure theory by David H. Fremlin, the paper by Heinz K¨onig on the generalized Radon–Nikod´ym theorem, the lecture notes by C.E. Heil on absolutely continuous functions, Dan Ma’s Topology Blog on exotic examples of topological spaces, and the paper by Gert K. Pedersen on the Haar measure were very helpful in preparing this manuscript.
Book Detail :-
Title: Measure and Integration
Edition:
Author(s): Dietmar A. Salamon
Publisher:
Series:
Year: 2020
Pages: 300
Type: PDF
Language: English
ISBN:
Country: US
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About Author :-
Author Dietmar A. Salamon (born 1953 in Bremen) is a German mathematician. He earned his PhD degree at the University of Bremen with with a thesis on control theory in 1982.
He subsequently spent two years as a postdoctoral fellow at the Mathematical Research Center at the University of Wisconsin–Madison, followed by one year at the Mathematical Research Institute at ETH Zurich. In 1986 he became a lecturer at the University of Warwick where he become the full professor in 1994. From 1998 to 2018 he was a full professor of mathematics at ETH Zurich, retiring as professor emeritus in 2018.
Salamon's field of research is symplectic topology (symplectic geometry), Gromov's pseudoholomorphic curves, Floer homology, and Seiberg-Witten invariants on four-dimensional manifolds.
All Famous Books of this Author :-
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• Download PDF Functional Analysis by Theo Buhler, Dietmar Salamon
• Download PDF Measure and Integration by Dietmar Salamon
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Book Contents :-
Measure and Integration written by
Dietmar A. Salamon
cover the following topics.
Introduction
Abstract Measure Theory
σ-Algebras, Measurable Functions, Integration of Nonnegative Functions, Integration of Real Valued Functions, Sets of Measure Zero, Completion of a Measure Space, Exercises
The Lebesgue Measure
Outer Measures, The Lebesgue Outer Measure, The Transformation Formula, Lebesgue Equals Riemann, Exercises
Borel Measures
Regular Borel Measures, Borel Outer Measures, The Riesz Representation Theorem, Exercises
Lp Spaces
Holder and Minkowski, The Banach Space Lp(µ), Separability, Hilbert Spaces, The Dual Space of Lp(µ), Exercises
The Radon–Nikod´ym Theorem
Absolutely Continuous Measures, The Dual Space of Lp(µ) Revisited, Signed Measures, Radon–Nikod´ym Generalized, Exercises
Differentiation
Weakly Integrable Functions, Maximal Functions, Lebesgue Points, Absolutely Continuous Functions, Exercises
Product Measures
The Product σ-Algebra, The Product Measure, Fubini’s Theorem, Fubini and Lebesgue, Convolution, Marcinkiewicz Interpolation, The Calder´on–Zygmund Inequality, Exercises
The Haar Measure
Topological Groups, Haar Measures
Urysohn’s Lemma
The Product Topology
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