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
- 1980: Donald L. Cohn: Measure Theory