Measure and Integration (2012-13)

Announcements: This course will take place in one period (period 3).

Intended audience: Third-year students

Textbook: Measures, Integrals and Martingales by Rene L. Schilling, Cambridge press (2011).
ISBN-13 978 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 Theorem.

Time and place: Classes will take place in room 027 Minnaert building
Tuesday: Lecture 9-11 and Exercises 11-13
Thursday: Lecture 13:15-15 and Exercises 15:15-17:00

Chapters to be covered: 1,2 (self reading), 3-13, and if time permits 16-19.

Exercises:  Solutions of selected exercises will be posted on this webpage.
There is one hand-in exercise per week.

Exams: There will be a quiz and a final exam

Exam dates:
-- Quiz: Thursday March 7 from 15-17 (during the exercise class). Quiz material: Chapters 3-9.
Open book exam, but you are only allowed to use the book of R. Schilling, Measures, Integrals and Martingales).

-- Final exam: Tuesday April 16 from 9-12 in BBL 201

-- Hertentamen: Thursday May 23 from 13:30-16:30 in BBL 205


Grades: Final grade=0.2H+0.4Q+0.4F (Q=quiz grade, F=final exam grade, H=hand-in exercises)


Material covered/to be covered:
Collegeweek 1 (week 6):
Tuesday 5 February: Chapter 3--Exercises p.20: 1, 2, 4, 8, 9, 11, 12.
Thursday 7 February: Chapter 4--Exercises p.28: 4,5,6,8,10,11,13.
  Due date Thursday 14 February (to be handed in during the exercise class)
Collegeweek 2 (week 7):
Tuesday 12 February: Chapter 5. Exercises  p.36: 2,4,5,7,8,9,10.
Thursday 14 February: Chapter 6. Exercises p.46: 3,4,5,7,8,9.
  Due date Thursday 21 February (to be handed in during the exercise class)
Collegeweek 3 (week 8):
Tuesday 19 February: Chapter 7. Exercises  p.54: 1,3,6,8,4,5,7,10 (work out the exercises in the given order).
Thursday 21 February: Chapter 8. Exercises p.66: 2, 3, 4, 5, 6 ,9, 12, 15.
Due date Thursday 28 February (to be handed in during the exercise class)

Collegeweek 4 (week 9):
Tuesday 26 February: Chapter 9. Exercises p.73: 1,5,6,7,8,9,10.
Thursday 28 February: Chapter 10. Exercises p.84: 2,3,5((i)-(iv)),7,9.
Due date Thursday 7 March (to be handed in during the exercise class)
Collegeweek 5 (week 10):
Tuesday 5 March: Chapter 11 (begin). Exercises: first finish the exercises of Chapter 10 and p.101: 1, 3, 4, 6.
Thursday 7 March: No lecture from 13-15. The quiz will take place from 15-17 (during the exercise class).
Quiz material: Chapters 3-9. Open book quiz, but you are only allowed to use the book of R. Schilling, Measures, Integrals and Martingales).


Collegeweek 6 (week 11):
No classes on Tuesday and Thursday (hertentamen week).

Collegeweek 7 (week 12):
Tuesday 19 March: Rest of Chapter 11. Exercises p.101: 7, 8, 12(i), 15 (assume that X is non-negative), 16.
Thursday 21 March: Chapter 12 (begin). Exercises p. 117: 1, 6, 7, 8, 10.
  Due date Thursday March 28 (to be handed in during the exercise class).

Collegeweek 8 (week 13):
Tuesday 26 March: Rest of Chapter 12 + beginning of Chapter 13. Exercises p. 117: 15, 21 + Exercises 130: 1, 2 +ExtraExercise (please bring a copy to the exercises).
Thursday 28 March: Rest of Chapter 13. Exercises p. 130: 4,  6, 7, 8(i), 9, 11, 12.
. Due date Thursday April 4 (to be handed in during the exercises)
Collegeweek 9 (week 14):
Tuesday April 2: NO LECTURE HOUR, but there is an exercise hour from 10-12 in Min 207: please finish all the exercises from Chapter 13.
Thursday April 4: Chapter 16 (till page  169). Exercises p. 173: 1, 2, 3, 4, 5.
No Hand in exercises.

Collegeweek 10 (week 15):
Tuesday April 9: Prove Theorem 16.6 (Vitali).  No new exercises, finish the exercises from the past weeks.
Tuesday April 11: Do a practice exam during the lecture hour.  Please bring a copy to the lecture hour
The Exercise hour is your last chance to finish all the exercises and to ask more questions on the Practice Exam.
Collegeweek 11 (week 16): Final exam: Tuesday April 16 from 9-12 in BBL 201. Open book exam, but you are only allowed to use the book of R. Schilling, Measures, Integrals and Martingales).