An Introduction to Lebesgue Integration and Fourier Series by Howard J. Wilcox (

Description: An Introduction to Lebesgue Integration and Fourier Series by Howard J. Wilcox, Ralph H. Fox Clear and concise introductory treatment for undergraduates covers Riemann integral, measurable sets and their properties, measurable functions, Lebesgue integral and convergence, pointwise conversion of Fourier series, other subjects. 1978 edition. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description This book arose out of the authors desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organised introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects.The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the students repertoire.Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration. Table of Contents Chapter 1. The Riemann Integral 1. Definition of the Riemann Integral 2. Properties of the Riemann Integral 3. Examples 4. Drawbacks of the Riemann Integral 5. Exercises Chapter 2. Measurable Sets 6. Introduction 7. Outer Measure 8. Measurable Sets 9. Exercises Chapter 3. Properties of Measurable Sets 10. Countable Additivity 11. Summary 12. Borel Sets and the Cantor Set 13. Necessary and Sufficient Conditions for a Set to be Measurable 14. Lebesgue Measure for Bounded Sets 15. Lebesgue Measure for Unbounded Sets 16. Exercises Chapter 4. Measurable Functions 17. Definition of Measurable Functions 18. Preservation of Measurability for Functions 19. Simple Functions 20. Exercises Chapter 5. The Lebesgue Integral 21. The Lebesgue Integral for Bounded Measurable Functions 22. Simple Functions 23. Integrability of Bounded Measurable Functions 24. Elementary Properties of the Integral for Bounded Functions 25. The Lebesgue Integral for Unbounded Functions 26. Exercises Chapter 6. Convergence and The Lebesgue Integral 27. Examples 28. Convergence Theorems 29. A Necessary and Sufficient Condition for Riemann Integrability 30. Egoroffs and Lusins Theorems and an Alternative Proof of the Lebesgue Dominated Convergence Theorem 31. Exercises Chapter 7. Function Spaces and GBP superscript 2 32. Linear Spaces 33. The Space GBP superscript 2 34. Exercises Chapter 8. The GBP superscript 2 Theory of Fourier Series 35. Definition and Examples 36. Elementary Properties 37. GBP superscript 2 Convergence of Fourier Series 38. Exercises Chapter 9. Pointwise Convergence of Fourier Series 39. An Application: Vibrating Strings 40. Some Bad Examples and Good Theorems 41. More Convergence Theorems 42. Exercises Appendix Logic and Sets Open and Closed Sets Bounded Sets of Real Numbers Countable and Uncountable Sets (and discussion of the Axiom of Choice) Real Functions Real Sequences Sequences of Functions Bibliography; Index Long Description Undergraduate-level introduction to Riemann integral, measurable sets, measurable functions, Lebesgue integral, other topics. Numerous examples and exercises. Details ISBN0486682935 Author Ralph H. Fox Short Title INTRO TO LEBESGUE INTEGRATION Language English ISBN-10 0486682935 ISBN-13 9780486682938 Media Book Imprint Dover Publications Inc. Place of Publication New York Country of Publication United States Illustrations 8ill. Format Paperback DOI 10.1604/9780486682938 UK Release Date 2003-03-17 AU Release Date 2003-03-17 NZ Release Date 2003-03-17 Pages 159 Publisher Dover Publications Inc. Edition Description Dover ed Year 2003 DEWEY 515.2433 Audience General Series Dover Books on Mathema 1.4tics Publication Date 2003-03-28 US Release Date 2003-03-28 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:78525833;

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