Measure and Integration: Examples, Concepts, and Applications instructs on core proofs, theorems, and approaches of real analysis as illustrated via compelling exercises and carefully crafted, practical examples. Following early chapters on core concepts and approaches of real analysis, the authors apply real analysis across integration on product spaces, radon functionals, bounded variation and lebesgue-stieltjes measures, convolutions, probability, and differential equations, among other topics. Advanced exercises are also included at the end of each chapter, with exercise difficulty level noted for instructors, and solutions included in an appendix.
From chapter one onward, students are asked to apply concepts to reinforce understanding and gain applied experience in real analysis. In particular, exercises challenge students to use key proofs of major real analysis theorems to encourage independent thinking, problem-solving, and new areas of research powered by real analysis.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Preface - p. ix 7. Chapter 1: Abstract integration - p. 1 8. Chapter 2: Construction of measures - p. 39 9. Chapter 3: Product measures - p. 75 10. Chapter 4: Complex and local measures - p. 89 11. Chapter 5: The Lebesgue-Radon-Nikodym theorem - p. 109 12. Chapter 6: Measures on locally compact Hausdorff spaces - p. 121 13. Chapter 7: Local Lebesgue-Stieltjes measures - p. 145 14. Chapter 8: The Fourier transform - p. 177 15. Chapter 9: Probability - p. 193 16. Chapter 10: Linear ODEs with measure coefficients - p. 227 17. Chapter 11: The boundary behavior of holomorphic functions - p. 249 18. Appendix A: Set theory - p. 267 19. Appendix B: Topological and metric spaces - p. 277 20. Appendix C: Algebra - p. 283 21. Appendix D: Analysis - p. 289 22. Appendix E: Functional analysis - p. 295 23. Appendix F: Complex analysis - p. 299 24. List of symbols - p. 303 25. References - p. 305 26. Index - p. 311
Measure and Integration: Examples, Concepts, and Applications instructs on core proofs, theorems, and approaches of real analysis as illustrated via compelling exercises and carefully crafted, practical examples. Following early chapters on core concepts and approaches of real analysis, the authors apply real analysis across integration on product spaces, radon functionals, bounded variation and lebesgue-stieltjes measures, convolutions, probability, and differential equations, among other topics. Advanced exercises are also included at the end of each chapter, with exercise difficulty level noted for instructors, and solutions included in an appendix.
From chapter one onward, students are asked to apply concepts to reinforce understanding and gain applied experience in real analysis. In particular, exercises challenge students to use key proofs of major real analysis theorems to encourage independent thinking, problem-solving, and new areas of research powered by real analysis.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Preface - p. ix 7. Chapter 1: Abstract integration - p. 1 8. Chapter 2: Construction of measures - p. 39 9. Chapter 3: Product measures - p. 75 10. Chapter 4: Complex and local measures - p. 89 11. Chapter 5: The Lebesgue-Radon-Nikodym theorem - p. 109 12. Chapter 6: Measures on locally compact Hausdorff spaces - p. 121 13. Chapter 7: Local Lebesgue-Stieltjes measures - p. 145 14. Chapter 8: The Fourier transform - p. 177 15. Chapter 9: Probability - p. 193 16. Chapter 10: Linear ODEs with measure coefficients - p. 227 17. Chapter 11: The boundary behavior of holomorphic functions - p. 249 18. Appendix A: Set theory - p. 267 19. Appendix B: Topological and metric spaces - p. 277 20. Appendix C: Algebra - p. 283 21. Appendix D: Analysis - p. 289 22. Appendix E: Functional analysis - p. 295 23. Appendix F: Complex analysis - p. 299 24. List of symbols - p. 303 25. References - p. 305 26. Index - p. 311
