Lebesgue Measure and Integration Theory: Foundations and Solved Exercises offers a thorough, engaging introduction to Lebesgue measure and the theory of integration for students of mathematics and physics. This book provides the complete theoretical underpinnings of this theory, with the corresponding proofs, adapted to the level of advanced undergraduate and graduate students in these disciplines. Beginning with a fundamental discussion of measure spaces, the book moves onto measurable and non-measurable sets, approximation of measurable sets, measurable functions, the Lebesgue integral, the relationship between differentiation and integration on R, and product measures, among other topics. Examples and solved exercises are included across chapters to reinforce understanding and application.
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. Dedication - p. v 7. List of figures - p. ix 8. Biography - p. xi 9. Preface - p. xiii 10. Chapter 1: Measure spaces - p. 1 11. Chapter 2: Measurable functions - p. 107 12. Chapter 3: The Lebesgue integral - p. 151 13. Chapter 4: The relationship between differentiation and integration - p. 261 14. Chapter 5: Product measures - p. 317 15. Bibliography - p. 353 16. Index - p. 355
Lebesgue Measure and Integration Theory: Foundations and Solved Exercises offers a thorough, engaging introduction to Lebesgue measure and the theory of integration for students of mathematics and physics. This book provides the complete theoretical underpinnings of this theory, with the corresponding proofs, adapted to the level of advanced undergraduate and graduate students in these disciplines. Beginning with a fundamental discussion of measure spaces, the book moves onto measurable and non-measurable sets, approximation of measurable sets, measurable functions, the Lebesgue integral, the relationship between differentiation and integration on R, and product measures, among other topics. Examples and solved exercises are included across chapters to reinforce understanding and application.
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. Dedication - p. v 7. List of figures - p. ix 8. Biography - p. xi 9. Preface - p. xiii 10. Chapter 1: Measure spaces - p. 1 11. Chapter 2: Measurable functions - p. 107 12. Chapter 3: The Lebesgue integral - p. 151 13. Chapter 4: The relationship between differentiation and integration - p. 261 14. Chapter 5: Product measures - p. 317 15. Bibliography - p. 353 16. Index - p. 355
