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An Introduction to Lebesgue Integration and Fourier Series by Howard J. Wilcox,David L. Myers ISBN: 0486682935 Dover Publications Price: $14.95 click here to see this book Undergraduate-level introduction to Riemann integral, measurable sets, measurable functions, Lebesgue integral, other topics. Numerous examples and exercises. Table of Contents for An Introduction to Lebesgue Integration and Fourier Series 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 The   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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