Real Analysis

A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.

N. L. Carothers (Author)

9780521497565, Cambridge University Press

Paperback, published 15 August 2000

416 pages, 45 b/w illus.
25.4 x 17.8 x 2.2 cm, 0.73 kg

'The author writes lucidly in a friendly, readable style and he is strong at motivating, anticipating and reviewing the various themes that permeate the text … The overwhelming impression is that Real analysis was a labour of love for the author, written with a genuine reverence for both its beautiful subject matter and its creators, refiners and teachers down the ages. As such - and high praise indeed - it will sit very happily alongside classics such as Apostol's Mathematical analysis, Royden's Real analysis, Rudin's Real and complex analysis and Hewitt and Stromberg's Real and abstract analysis.' The Mathematical Gazette

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. 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.

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.

Subject Areas: Real analysis, real variables [PBKB]