Measure and Integration (2007)
Classes will begin in week 7.
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 K11 and Thursday from 11-13 in K11.
On Tuesday March 27, the lecture will be in
BBL 105, and on Thursday March 29, the
exercises will be in MIN 012.
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 17 (week
16) from 9-12 in room K11.
-- Final exam: Tuesday July 3 from 9-12
in UNNIK 211.
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: 3,6,7,8,4,5,10 (work out the
exercises in the given order).
Week
12: No classes (no
lecture and no
exercises)
(hertentamen
week).
Week 13: Chapter 8. Exercises p.65:
2, 3, 4, 5, 6 ,9, 12, 15. On
Tuesday March 27, the lecture will be in BBL 105, and on Thursday March
29, the
exercises will be in MIN 012.
Week 14: Chapter 9. Exercises
p.73: 1,3,5,6,7,8,9,10.
Week 15: On Tuesday: mid-term preparation extraexercises. There is no class on
Thursday.
Week 16: Mid-term (you will be
tested on the material covered in chapters 3,4,5,6,7,8,9). Tuesday April
17 from 9-12 in room K11. (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: Chapter 11(begin). Exercises p.100: 1, 3, 4, 6, 7
Week 19: rest of Chapter 11. Exercises p.101: 8, 12(i), 15
(assume that X is non-negative), 16.
Week 20: No classes on Tuesday
and Thursday.
Week 21: Chapter 12. Exercises p. 116: 1,
10, 21, 6, 7 (work
out the
exercises in the given order).
Week 22: No
classes (hertentamen week).
Week 23: Rest of 12 and 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: Tuesday: Preparation for
Final exam.
Week 27:
Final exam on Tuesday July 3 from
9-12 in UNNIK
211. Open book
exam, but you are only allowed
to use the book of
R. Schilling, Measures, Integrals and Martingales).
Solutions to selected exercises in the
book
Chapter3
Chapter4
Chapter5
Chapter6
Chapter7
Chapter8
Chapter9
solutions extra exercises
Chapter10
Chapter11
Chapter11extra
Chapter12
solutions extraexercises13
Chapter13
Chapter13