N. L. CarothersCambridge University Press, 8/21/2008EAN 9780521497565, ISBN10: 0521497566Paperback, 416 pages, 25.4 x 17.8 x 2.4 cmLanguage: EnglishThis 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. The course consists of three major topics: metric and normed linear spaces, function spaces, and Lebesgue measure and integration on the line. In an informal style, the author gives motivation and overview of new ideas, while supplying full details and proofs. He includes historical commentary, recommends articles for specialists and non-specialists, and provides exercises and suggestions for further study. This text for a first graduate course in real analysis was written to accommodate the heterogeneous audiences found at the masters level: students interested in pure and applied mathematics, statistics, education, engineering, and economics.PrefacePart I. Metric Spaces1. Calculus review2. Countable and uncountable sets3. Metrics and norms4. Open sets and closed sets5. Continuity6. Connected sets7. Completeness8. Compactness9. CategoryPart II. Function Spaces10. Sequences of functions11. The space of continuous functions12. The Stone-Weierstrass theorem13. Functions of bounded variation14. The Riemann-Stieltjes integral15. Fourier seriesPart III. Lebesgue Measure and Integration16. Lebesgue measure17. Measurable functions18. The Lebesgue integral19. Additional topics20. DifferentiationReferencesIndex.
Related
Related
Related
Related