Book:Donald L. Cohn/Measure Theory/Second Edition

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Donald L. Cohn: Measure Theory (2nd Edition)

Published $\text {2013}$.


Subject Matter


Contents

1 Measures
1.1 Algebras and Sigma-Algebras
1.2 Measures
1.3 Outer Measures
1.4 Lebesgue Measure
1.5 Completeness and Regularity
1.6 Dynkin Classes
2 Functions and Integrals
2.1 Measurable Functions
2.2 Properties That Hold Almost Everywhere
2.3 The Integral
2.4 Limit Theorems
2.5 The Riemann Integral
2.6 Measurable Functions Again, Complex-Valued Functions, and Image Measures
3 Convergence
3.1 Modes of convergence
3.2 Normed Spaces
3.3 Definitions of $\LL^p$ and $L^p$
3.4 Properties of $\LL^p$ and $L^p$
3.5 Dual Spaces
4 Signed and Complex Measures
4.1 Signed and Complex Measures
4.2 Absolute Continuity
4.3 Singularity
4.4 Functions of Finite Variation
4.5 The Duals of $L^p$ spaces
5 Product Measures
5.1 Constructions
5.2 Fubini's Theorems
5.3 Applications
6 Differentiation
6.1 Change of Variable in $\R^d$
6.2 Differentiation of Measures
6.3 Differentiation of Functions
7 Measures on Locally Compact Spaces
7.1 Locally Compact Spaces
7.2 The Riesz Representation Theorem
7.3 Signed and Complex Measures; Duality
7.4 Additional Properties of Regular Measures
7.5 The $\mu^\ast$-Measurable Sets and the Dual of $L^1$
7.6 Products of Locally Compact Spaces
7.7 The Daniell-Stone Integral
8 Polish Spaces and Analytic Sets
8.1 Polish Spaces
8.2 Analytic Sets
8.3 The Separation Theorem and Its Consequences
8.4 The Measurability of Analytic Sets
8.5 Cross Sections
8.6 Standard, Analytic, Lusin and Souslin Spaces
9 Haar Measure
9.1 Topological Groups
9.2 The Existence and Uniqueness of Haar Measure
9.3 Properties of Haar Measure
9.4 The Algebras $\map {L^1} G$ and $\map M G$
10 Probability
10.1 Basics
10.2 Laws of Large Numbers
10.3 Convergence in Distribution and the Central Limit Theorem
10.4 Conditional Distributions and Martingales
10.5 Brownian Motion
10.6 Construction of Probability Measures
A Notation and Set Theory
B Algebra and Basic Facts About $\R$ and $\C$
C Calculus and Topology in $\R^d$
D Topological Spaces and Metric Spaces
E The Bochner Integral
F Liftings
G The Banach-Tarski Paradox
H The Henstock-Kurzweil and McShane Integrals
References
Index of notation
Index


Further Editions