Book:Charalambos D. Aliprantis/Principles of Real Analysis/Third Edition
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Charalambos D. Aliprantis and Owen Burkinshaw: Principles of Real Analysis (3rd Edition)
Published $\text {1998}$, Academic Press
- ISBN 978-0120502578
Subject Matter
Contents
- Preface
- Chapter 1. Fundamentals of Real Analysis
- 1. Elementary Set Theory I
- 2. Countable and Uncountable Sets
- 3. The Real Numbers
- 4. Sequences of Real Numbers
- 5. The Extended Real Numbers
- 6. Metric Spaces
- 7. Compactness in Metric Spaces
- Chapter 2. Topology and Continuity
- 8. Topological Spaces
- 9. Continuous Real-Valued Functions
- 10. Separation Properties of Continuous Functions
- 11. The Stone-Weierstrass Approximation Theorem
- Chapter 3. The Theory of Measure
- 12. Semirings and Algebras of Sets
- 13. Measures on Semirings
- 14. Outer Measures and Measurable Sets
- 15. The Outer Measure Generated by a Measure
- 16. Measurable Functions
- 17. Simple and Step Functions
- 18. The Lebesgue Measure
- 19. Convergence in Measure
- 20. Abstract Measurability
- Chapter 4. The Lebesgue Integral
- 21. Upper Functions
- 22. Integrable Functions
- 23. The Riemann Integral as a Lebesgue Integral
- 24. Applications of the Lebesgue Integral
- 25. Approximating Integrable Functions
- 26. Product Measures and Iterated Integrals
- Chapter 5. Normed Spaces and $L_p$-spaces
- 27. Normed Spaces and Banach Spaces
- 28. Operators Between Banach Spaces
- 29. Linear Functionals
- 30. Banach Lattices
- 31. $L_p$-Spaces
- Chapter 6. Hilbert Spaces
- 32. Inner Product Spaces
- 33. Hilbert Spaces
- 34. Orthonormal Bases
- 35. Fourier Analysis
- Chapter 7. Special Topics in Integration
- 36. Signed Measures
- 37. Comparing Measures and the Radmi-Nikodym Theorem
- 38. The Riesz Representation Theorem
- 39. Differentiation and Integration
- 40. The Change of Variables Formula
- Bibliography
- List of Symbols
- Index