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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

### Table of Contents

**Download chapters as PDF**

**Front/Back Matter**

**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. Hausdorffâ€™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. Sardâ€™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