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 BBL 160 en Thursday from 9-11 in BBL 160 (please note the time change of the exercise hours) .  On Tuesday March 14, the lecture will be held in K11.

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: Tuesday April 18 (week 16) from 9-12 in Rupp (Trans.1) blauwe zaal.
--Finalexam: Tuesday July 4 (week 27) from 9-12 in Rupp (Trans.1) blauwe zaal.
--Hertentamen: Tuesday August 29 (week 35) from 9-12 in WG 611.

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: 3,6,8,4,5,10 (work out the exercises in the given order).  On Tuesday March 14, the lecture will be held in K11.
Week 12: No classes (no lecture and no exercises)  (hertentamen week).
Week 13: Rest of Chapter 7 + beginning of Chapter 8. Exercises p.54 exercise 7 and  p.65: 2, 6 ,9, 15.
Week 14: Rest of Chapter 8. Exercises p. 65: 3,4,5,12 en p. 73: 3, 6.
Week 15: On Tuesday: mid-term preparation extraproblems, solutionsextraproblems, and no class on Thursday, but I am available in my room (505-wiskunde gebouw) for more questions.
Week 16: Mid-term. Tuesday April 18  from 9-12 in Rupp (Trans.1) blauwe zaal.  (Open book exam, but you are only allowed to use the book of R. Schilling, Measures, Integrals and Martingales).
Week 17: No classes (no lecture and no exercises).
Week 18: Chapter 9.  Exercises p.73: 1,5,7,8,9,10.
Week 19: Chapter 10. Exercises p.84: 2,3,5((i)-(iv)),7,9.
Week 20: Chapter 11. Exercises p.100: 1,3,4,6,8(i,iii),12(i),16.
Week 21:No classes (no lecture and no exercises)  (hertentamen week).
Week 22: rest of Chapter 11+beginning of Chapter 13. Exercises p.130: 1,2 + extraexercises
Week 23: Chapter 13. Exercises p.130: 4,7,9
Week 24: rest of Chapter 13. Exercises p.130: 6, 8(i) en 12.
Week 25: Chapter 12.  Exercises p.116: 1(in part (i) assume that u in L^p(\mu)), 6, 7, 10.
Week 26: Final preparation on Tuesday.   No classes on Thursday, but I am available for questions from 10-11 in my office (room 505, math building).
Week 27: Final exam on Tuesday July 4 from 9-12 in Blauwe zaal Trans.I (Rupp. gebouw). (Open book exam, but you are only allowed to use the book of R. Schilling, Measures, Integrals and Martingales).