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.
Extra Exercises (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).
If
you want to practice more for the final, here are more exercises.
Solutions
to selected exercises
Chapter3
Chapter4
Chapter5
Chapter6
Chapter7
Chapter8
Chapter9
Extra
Exercises
Chapter10
Chapter11
Chapter12
solutions
extraexercises13
Chapter13
Chapter13
Solutions Extra Exercises
solutions more exercises