Measure and Integration (2008)

Announcements:
Classes will begin in week 7.
Week 12 (March 18 and March 20): No classes (hertentamen week).
Week 22 (May 27 and May 29): No classes (hertentamen week).
Week 26 No classes on Tuesday June 24.  Exam preparation on Thursday June 26.

Intended audience: Third-year students

Textbook: Measures, Integrals and Martingales by Rene L. Schilling, Cambridge press (2005). ISBN 0-521-61525-9.

Outline: An introduction to abstract measure and integration theory.

Prerequisites: Standard first and second-year analysis courses.

Main subjects: Lebesgue measure in Euclidean space, measure and integration in abstract spaces, products of measures,  changes of variable, basic inequalities, Radon-Nikodym.

Time and place: Classes will be held on Tuesday from 11-13 in 611AB (lecture) and Thursday from 11-13 in 611AB (exercises).

Chapters to be covered: 1,2 (self reading), 3-13.

Exercises: Solutions of selected exercises will be posted on this webpage.

Exams: There will be two written exams given at the end of each period.

Exam dates:
--Midterm: Wednesday April 16 from 14-17 in Ruppert gebouw (Trans. 1) room 042. (Chapters3-9)

-- Final exam: Wednesday July 2 from 14-17 in Ruppert gebouw (Trans. 1) room 042. (Chapters 10-13)


-- Hertentamen: Wednesday August 20 from 14-17 in Aard C008. (Chapters 3-13)


Grades: Final grade is the average of the grades of the two written exams.


Material covered/to be covered:

Week 7: Chapter 3.  Exercises p.20: 1, 2, 4, 8, 11, 12.
 Week 8: Chapter 4.  Exercises p.28: 4,5,6,8,10,11,13
Week 9: Chapter 5. Exercises  p.36: 2,4,5,7,8,9,10.
Week 10: Chapter 6. Exercises p.46: 3,4,5,7,8,9.
Week 11: Chapter 7. Exercises p.54: 1,3,6,8,4,5,7,10 (work out the exercises in the given order).
Week 12: No classes (hertentamen week).
 Week 13: Chapter 8. Exercises p.65: 2, 3, 4, 5, 6 ,9, 15.
Week 14: rest of Chapter 8 and Chapter 9. Exercises p.65: 12 and p.73: 1,5,6,7,8,9,10.
Week 15: Rest of Chapter 9, and mid-term preparation. Extra Exercises.
Week 16: Mid-Term Wednesday April 16 from 14-17 in Ruppert gebouw (Trans. 1) room 042. (Chapters 3-9:  Open book exam, but you
are only allowed to use the book of R. Schilling, Measures, Integrals and Martingales).
Week 17: Chapter 10. Exercises p.84: 2,3,5((i)-(iv)),7,9.
Week 18: rest of Chapter 10. No exercises.
Week 19: Chapter 11. Exercises p.100: 1, 3, 4, 6, 7, 8.
Week 20: rest of Chapter 11, beginning of Chapter 12. Exercises p.100: 12(i), 15 (assume that X is non-negative), 16.
Week 21: Chapter 12. Exercises p. 116: 1, 10, 21, 6, 7 (work out the exercises in the given order).
Week 22: NO CLASSES=NO Lecture hour and No Exercise hour.
Week 23: Rest of Chapter 12 + beginning of Chapter 13. Exercises p. 117: 8, 15 and extraexercises13
Week 24:  Chapter 13. Exercises p. 130: 1, 2, 4, 7, 8(i).
Week 25: rest of Chapter 13. p. 130: 6, 9, 11, 12.
Week 26: Final exam Preparation. No class on Tuesday. Exam preparation on Thursday.  (please bring a copy with you on Thursday).
Week 27: Final Exam on Wednesday July 2 from 14-17 in Ruppert gebouw (Trans. 1) room 042. Open book exam, but you
are only allowed to use the book of R. Schilling, Measures, Integrals and Martingales).