# An Introduction to Lebesgue Integration and Fourier Series

## Wilcox, Howard J.; Myers, David L.

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Undergraduate-level introduction to Riemann integral, measurable sets, measurable functions, Lebesgue integral, other topics. Numerous examples and exercises.

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Contenuti:

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. Egoroff's and Lusin's Theorems and an Alternative Proof of the Lebesgue Dominated Convergence Theorem 31. Exercises Chapter 7. Function Spaces and £ superscript 2 32. Linear Spaces 33. The Space £ superscript 2 34. Exercises Chapter 8. The £ superscript 2 Theory of Fourier Series 35. Definition and Examples 36. Elementary Properties 37. £ 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

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## 1.An Introduction to Lebesgue Integration and Fourier Series

Editore: Dover Pubns (1994)
ISBN 10: 0486682935 ISBN 13: 9780486682938
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Descrizione libro Dover Pubns, 1994. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria V0-9780486682938

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## 2.An Introduction to Lebesgue Integration and Fourier Series Format: Trade Paper

Editore: Dover Publishers
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Descrizione libro Dover Publishers. Condizione libro: New. Brand New. Codice libro della libreria 0486682935

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## 3.An Introduction to Lebesgue Integration and Fourier Series

Editore: Dover Publications Inc. (1995)
ISBN 10: 0486682935 ISBN 13: 9780486682938
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Descrizione libro Dover Publications Inc., 1995. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IQ-9780486682938

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## 4.Introduction to Lebesgue Integration and Fourier Series

ISBN 10: 0486682935 ISBN 13: 9780486682938
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Descrizione libro Paperback. Condizione libro: New. This item is printed on demand. Item doesn't include CD/DVD. Codice libro della libreria 972736

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## 5.An Introduction to Lebesgue Integration and Fourier Series (Paperback)

Editore: Dover Publications Inc., United States (1995)
ISBN 10: 0486682935 ISBN 13: 9780486682938
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Descrizione libro Dover Publications Inc., United States, 1995. Paperback. Condizione libro: New. Dover ed. 231 x 155 mm. Language: English . Brand New Book ***** Print on Demand *****. This clear and concise introductory treatment for undergraduates covers the Riemann integral, measurable sets and their properties, measurable functions, the Lebesgue integral and convergence, pointwise conversion of the Fourier series, and other subjects. Numerous examples and exercises supplement the text. Basic knowledge of advanced calculus is the sole prerequisite. 1978 edition. Codice libro della libreria APC9780486682938

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## 6.An Introduction to Lebesgue Integration and Fourier Series (Paperback)

Editore: Dover Publications Inc., United States (1995)
ISBN 10: 0486682935 ISBN 13: 9780486682938
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Descrizione libro Dover Publications Inc., United States, 1995. Paperback. Condizione libro: New. Dover ed. 231 x 155 mm. Language: English . Brand New Book ***** Print on Demand *****.This clear and concise introductory treatment for undergraduates covers the Riemann integral, measurable sets and their properties, measurable functions, the Lebesgue integral and convergence, pointwise conversion of the Fourier series, and other subjects. Numerous examples and exercises supplement the text. Basic knowledge of advanced calculus is the sole prerequisite. 1978 edition. Codice libro della libreria APC9780486682938

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## 7.An Introduction to Lebesgue Integration and Fourier Series (Dover Books on Advanced Mathematics)

Editore: Dover Publications Inc. 1995-02-01 (1995)
ISBN 10: 0486682935 ISBN 13: 9780486682938
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Descrizione libro Dover Publications Inc. 1995-02-01, 1995. Condizione libro: New. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Codice libro della libreria NU-ING-00601226

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## 8.An Introduction to Lebesgue Integration and Fourier Series (Dover Books on Mathematics)

Editore: Dover Publications (1995)
ISBN 10: 0486682935 ISBN 13: 9780486682938
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Descrizione libro Dover Publications, 1995. Condizione libro: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: 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. Egoroff's and Lusin's Theorems and an Alternative Proof of the Lebesgue Dominated Convergence Theorem 31. Exercises Chapter 7. Function Spaces and superscript 2 32. Linear Spaces 33. The Space superscript 2 34. Exercises Chapter 8. The superscript 2 Theory of Fourier Series 35. Definition and Examples 36. Elementary Properties 37. 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. Codice libro della libreria ABE_book_new_0486682935

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## 9.Introduction to Lebesgue Integration and Fourier Series

Editore: Dover Publications
ISBN 10: 0486682935 ISBN 13: 9780486682938
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Descrizione libro Dover Publications. Paperback. Condizione libro: New. Paperback. 192 pages. Dimensions: 9.1in. x 6.1in. x 0.4in.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-organized 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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Codice libro della libreria 9780486682938

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## 10.An Introduction to Lebesgue Integration and Fourier Series (Dover Books on Mathematics)

Editore: Dover Publications (1995)
ISBN 10: 0486682935 ISBN 13: 9780486682938
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Descrizione libro Dover Publications, 1995. Paperback. Condizione libro: New. Codice libro della libreria INGM9780486682938

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