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Measure Theory and Integration

About this Title

Michael E. Taylor, University of North Carolina, Chapel Hill, Chapel Hill, NC

Publication: Graduate Studies in Mathematics
Publication Year: 2006; Volume 76
ISBNs: 978-0-8218-4180-8 (print); 978-1-4704-1155-8 (online)
DOI: https://doi.org/10.1090/gsm/076
MathSciNet review: MR2245472
MSC: Primary 28-01; Secondary 28Axx, 28C05, 28D05, 46-01, 60-01, 60J65

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Table of Contents

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Front/Back Matter

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Chapters

• Chapter 1. The Riemann integral
• Chapter 2. Lebesgue measure on the line
• Chapter 3. Integration on measure spaces
• Chapter 4. $L^p$ spaces
• Chapter 5. The Caratheodory construction of measures
• Chapter 6. Product measures
• Chapter 7. Lebesgue measure on $\mathbb {R}^n$ and on manifolds
• Chapter 8. Signed measures and complex measures
• Chapter 9. $L^p$ spaces, II
• Chapter 10. Sobolev spaces
• Chapter 11. Maximal functions and a.e. phenomena
• Chapter 12. Hausdorff’s $r$-dimensional measures
• Chapter 13. Radon measures
• Chapter 14. Ergodic theory
• Chapter 15. Probability spaces and random variables
• Chapter 16. Wiener measure and Brownian motion
• Chapter 17. Conditional expectation and martingales
• Appendix A. Metric spaces, topological spaces, and compactness
• Appendix B. Derivatives, diffeomorphisms, and manifolds
• Appendix C. The Whitney Extension Theorem
• Appendix D. The Marcinkiewicz Interpolation Theorem
• Appendix E. Sard’s Theorem
• Appendix F. A change of variable theorem for many-to-one maps
• Appendix G. Integration of differential forms
• Appendix H. Change of variables revisited
• Appendix I. The Gauss-Green formula on Lipschitz domains