Real Analysis [Paperback]

A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.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.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.This course in real analysis is 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 of value to specialists and nonspecialists alike. The text covers three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal, down-to-earth style, the author gives motivation and overview of new ideas, while still supplying full details and complete proofs. He provides a great many exercises and suggestions for further study.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 Il#§