Real Analysis (Paperback)

Preface; Part I. Metric Spaces: 1. Calculus review; 2. Countable and uncountable sets; 3. Metrics and norms; 4. Open sets and closed sets; 5. Continuity; 6. Connected sets; 7. Completeness; 8. Compactness; 9. Category; Part II. Function Spaces: 10. Sequences of functions; 11. The space of continuous functions; 12. The Stone-Weierstrass theorem; 13. Functions of bounded variation; 14. The Riemann-Stieltjes integral; 15. Fourier series; Part III. Lebesgue Measure and Integration: 16. Lebesgue measure; 17. Measurable functions; 18. The Lebesgue integral; 19. Additional topics; 20. Differentiation; References; Index.