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An Introduction to Measure and Integration: Second Edition

About this Title

Inder K. Rana, Indian Institute of Technology, Powai, Mumbai, India

Publication: Graduate Studies in Mathematics
Publication Year: 2002; Volume 45
ISBNs: 978-0-8218-2974-5 (print); 978-1-4704-2096-3 (online)
DOI: https://doi.org/10.1090/gsm/045
MathSciNet review: MR1934675
MSC: Primary 28-01

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Table of Contents

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Front/Back Matter

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Chapters

• Prologue. The length function
• Chapter 1. Riemann integration
• Chapter 2. Recipes for extending the Riemann integral
• Chapter 3. General extension theory
• Chapter 4. The Lebesgue measure on $\mathbb {R}$ and its properties
• Chapter 5. Integration
• Chapter 6. Fundamental theorem of calculus for the Lebesgue integral
• Chapter 7. Measure and integration on product spaces
• Chapter 8. Modes of convergence and $L_p$-spaces
• Chapter 9. The Radon-Nikodym theorem and its applications
• Chapter 10. Signed measures and complex measures
• Appendix A. Extended real numbers
• Appendix B. Axiom of choice
• Appendix C. Continuum hypotheses
• Appendix D. Urysohn’s lemma
• Appendix E. Singular value decomposition of a matrix
• Appendix F. Functions of bounded variation
• Appendix G. Differentiable transformations