Measure and Integration (2013-14)

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 on
Monaday: Lecture 9-11 in room BBL 079 and Exercises 11-13 in room BBL 065 (room change from BBL165 to BBL065)
Wednesday: Lecture 9-11 in room 611 (Math building) and Exercises 11-13 in Min 022.

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

-- Quiz: Wednesday March 5 from 11-13 (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: Monday April 14 from 9-12 in BBL 001.

-- Hertentamen: May 28 from 9-12 in BBL 007.

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

Announcements: Starting from Monday February 10, the room for the exercise hour is BBL065 instead of BBL165, except on Monday April 7 the room will be BBL 165.

Material covered/to be covered:
Collegeweek 1 (week 6):
Monday February 3: Chapter 3--Exercises p.20: 1, 2, 4, 8, 9, 11, 12.
Wednesday February 5: Chapter 4--Exercises p.28: 4,5,6,8,10,11,13.
Hand-in   Due date Wednesday February 12 (to be handed in during the exercise class)
Collegeweek 2 (week 7):
Monday February 10: Chapter 5. Exercises  p.36: 2,4,5,7,8,9,10.
Wednesday February 12: Chapter 6. Exercises p.46: 3,4,5,7,8,9. 
Hand-in  Due date Wednesday February 19 (to be handed in during the exercise class)

Collegeweek 3 (week 8):
Monday February 17: Chapter 7. Exercises  p.54: 1,3,6,8,4,5,7,10 (work out the exercises in the given order).Wednesday February 19: Chapter 8. Exercises p.66: 2, 3, 4, 5, 6 ,9, 12, 15. 
Hand-in    Due date Wednesday February 26 (to be handed in during the exercise class)

Collegeweek 4 (week 9):
Monday February 24: Chapter 9. Exercises p.73: 1,5,6,7,8,9,10. 
Wednesday February 26: Chapter 10. Exercises p.84: 2,3,5((i)-(iv)),7,9. 
Hand-in   Due date Monday March 3 (to be handed in during the exercise class)
Collegeweek 5 (week 10):
Monday March 3: Chapter 11 (begin). Exercises: first finish the exercises of Chapter 10 and p.101: 1, 4, 6, 8. 
Wednesday March 5: No lecture from 9-11. The quiz will take place from 11-13 (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 Monday and Wednesday (hertentamen week).

Collegeweek 7 (week 12):
Tuesday 19 March: Rest of Chapter 11. Exercises p.101: 7, 8, 12, 15 (assume that X is non-negative), 16. 
Thursday 21 March: Chapter 12. Exercises p. 117: 1, 6, 7, 8, 10, 15, 21.
Hand-in     Due date Wednesday March 26 (to be handed in during the exercise class).
Collegeweek 8 (week 13):
Mannday March 24: Rest of Chapter 12 + beginning of Chapter 13. Exercises p. 117: 11, 14 + Exercises 130: 1, 2 +ExtraExercise (please bring a copy to the exercises). 
Wednesday March 26: Rest of Chapter 13. Exercises p. 130: 4,  6, 7, 8(i), 9, 11, 12. 
Hand-in     Due date Wednesday April 2 (to be handed in during the exercises)
 
Collegeweek 9 (April 2week 14):
Tuesday March 31: Rest of Chapter 13 + Chapter 16 (till page 169). Exercises p. 173: 1, 2, 3, 4, 5, 7(i, ii), 10.
Thursday April 2: Radon-Nikodym Theorem, the lecture notes are chapters SignedMEasures.pdf  and RadonNikodym.pdf   from the book of Richard Bass, Analysis for Graduate Students.  exercisesRadonNikodym.pdf  
Hand-in  Due date Wednesday April 9 (to be handed in during the exercises)
Collegeweek 10 (week 15):
Tuesday April 7: Rest of Radon-Nikodym (hoorcollege aantekeningen RadonNikodymSignedMeasures.pdf  ).  No new exercises, finish the exercises from the past weeks.
Tuesday April 9: NO Lecture hour, so class begins at 11 with the exercise hour. Do a practice exam   .  Please bring a copy to the exercise hour.

Collegeweek 11 (week 16): Final exam: Monday April 14 from 9-12 in BBL 001. Open book exam, but you are only allowed to use the book of R. Schilling, Measures, Integrals and Martingales) and the additional chapters on Signed measures and Radon Nikodym Theorem.