Real Analysis

Klappentext A text for a first graduate course in real analysis for students in pure and applied mathematics! statistics! education! engineering! and economics. Zusammenfassung This is a course in real analysis directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus! the book offers something to specialists and non-specialists alike! including historical commentary! carefully chosen references! and plenty of exercises. Inhaltsverzeichnis 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.

Zusammenfassung
This is a course in real analysis directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something to specialists and non-specialists alike, including historical commentary, carefully chosen references, and plenty of exercises.

Inhalt
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.

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