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Title: An Introduction to Lebesgue Integration and Fourier Series (Dover Books on Advanced Mathematics) by Howard J. Wilcox, David L. Myers ISBN: 0-486-68293-5 Publisher: Dover Publications Pub. Date: 01 November, 1994 Format: Paperback Volumes: 1 List Price(USD): $11.95 |
Average Customer Rating: 3.67 (3 reviews)
Rating: 4
Summary: Gentle Intro to Measure Theory
Comment: I am using this book with two advanced undergraduates, after working through a basic introduction to analysis text the previous semester. Each section is about 3 or 4 pages long, giving the main results and most proofs, although some are left as exercises. Each chapter ends with a nice set of exercises, most of which are accessible to students who feel comfortable with epsilon/delta proofs. The book is very short and concise, 145 pages plus an appendix summarizing basic analysis results on sets, countability, functions, and sequences.
Chapter 1 reviews the Riemann integral and some of its drawbacks. Chapter 2 introduces the idea of outer measure and measurable sets, all on the unit interval. The next two chapters discuss properties of measurable sets and measurable functions. Chapters 5 and 6 then cover the Lebesgue integral and convergence theorems. The last three chapers introduce L2 spaces, Fourier series, and proofs of convergence.
All in all this is a good, very cheap way to learn the basics of measure theory and the Lebesgue integral, before moving on to something like Rudin or Royden.
Rating: 4
Summary: direct intuitive treatment but much "left as an exercise"
Comment: This assumes some advanced calculus and then introduces enough Lebesgue integration amd measure theory to explain and prove the basic convergence results for (generalized) Fourier analysis. Second half of second year and above.
Everything is very well motivated and the book is not long, but quite a lot is "left as an exercise for the reader." This really hurts the book for self study in my view. If you have a bigger book on real analysis and want another treatment, or need a refresher this will do nicely. On its own -- you've been warned.
Rating: 3
Summary: A good basic introduction to Lebesgue integration
Comment: A good basic introduction to Lebesgue integration, but a little sketchy in some places. Each chapter concludes with a good set of exercises. This book is good for getting the "idea" behind Lebesgue integration, but comes up short on many of the details. An excellent companion volume would be Jones' "Lebesgue Integration on Euclidean space".
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Title: Introductory Real Analysis by A. N. Kolmogorov, S. V. Fomin ISBN: 0486612260 Publisher: Dover Publications Pub. Date: 01 June, 1975 List Price(USD): $15.95 |
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Title: Elementary Real and Complex Analysis (Dover Books on Mathematics) by Georgi E. Shilov, Richard A. Silverman ISBN: 0486689220 Publisher: Dover Publications Pub. Date: 01 February, 1996 List Price(USD): $19.95 |
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Title: Elements of the Theory of Functions and Functional Analysis by A. N. Kolmogorov, S. V. Fomin ISBN: 0486406830 Publisher: Dover Publications Pub. Date: 01 March, 1999 List Price(USD): $12.95 |
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Title: Complex Variables: Harmonic and Analytic Functions by Francis J. Flanigan ISBN: 0486613887 Publisher: Dover Publications Pub. Date: 01 February, 1983 List Price(USD): $14.95 |
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Title: Elementary Functional Analysis by Georgi E. Shilov, Richard A. Silverman ISBN: 0486689239 Publisher: Dover Publications Pub. Date: 01 January, 1996 List Price(USD): $15.95 |
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