Measure and Integration 2016-17
Lecturer: Karma Dajani
(k.dajani1@uu.nl)
Student assistents:Pol van
Hoften (p.vanhoften@uu.nl or pol_1337@live.nl )
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
Wednesday: Lecture 13.15-15.00 in BBG 169 and Exercises 15.15-17.00
in BBG 205.
Friday: Lecture 11.00-12.45 in BBG 169 and Exercises 13.15-15.00 in
in BBG 205.
Chapters to be covered: 1,2
(self reading), 3-13, 16 + extra lecture notes on the Theorem
of Radon-Nikodym.
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: Friday
October 14 (Chapters 3-9) from 11-13 in Unnik 211.
Open book exam, but you are only allowed to use the book of R.
Schilling, Measures, Integrals and Martingales).
--Reparation Quiz: Only
applies to students with a quiz grade lower than a 7. On
Friday
October 28 from 13-15 there will be a reparation quiz in room
BBL165.
Depending on the number of correct answered questions, your grade
can
be pushed to a maximum of a 7
-- Final exam: Wednesday
09/11/2016 from 16:00-19:00 in EDUC (THEATRON)
-- Hertentamen: Friday
06/01/2017 from 13:30-16:30 in UNNIK 211.
Grades: Final grade=0.2H+0.3Q+0.5F (Q=quiz grade, F=final
exam grade, H=hand-in exercises).
Material covered/to be covered:
Collegeweek 1 (week 37):
Wednesday September 14: Chapter 3--Exercises p.20: 1, 2, 4, 8, 9,
11, 12.
Friday September 16: Chapter 4--Exercises p.28: 4, 5, 6, 8, 10, 11,
13.
Hand-in Exercise 1 due date Friday September 23.
Collegeweek 2 (week 38):
Wednesday September 21: Chapter 5. Exercises p.36:
2,4,5,7,8,9,10.
Friday September 23: Chapter 6. Exercises p.46: 3, 4, 5, 7, 8,
9.
Hand-in exercise 2
due date Friday
September 30.
Collegeweek 3 (week 39):
Wednesday September 28: Chapter 7. Exercises p.54:
1,3,6,8,4,5,7,10 (work out the exercises in the given order).
Friday September 30: Chapter 8. Exercises p.66: 2, 3, 4, 5, 6 ,9,
12, 15.
Hand in exercise
(to be handed in during the exercise class) due date Friday
October 7
Collegeweek 4 (week 40):
Wednesday October 5: Chapter 9. Exercises p.73:
1,5,6,7,8,9,10.
Friday October 7: Chapter 10. Exercises p.84:
2,3,5((i)-(iv)),7,9.
Hand in exercise Due date
Friday Friday October 21 during the Exercise hour.
Collegeweek 5 (week 41):
Wednesday October 12: Chapter 11. Exercises p.101: 1, 4, 6, 7, 8,
12, 15 (assume that X is non-negative), 16.
Friday October 14: Quiz from
11-13 (during the lecture class in Unnik 211). For students who
have the right for extra time the quiz begins at 10:30 in UNNIK
201, and at 10:50 we move to UNNIK 211.
Quiz material: Chapters 3-9.
Open
book quiz, but you are only allowed to use the book of R.
Schilling,
Measures, Integrals and Martingales).
No new exercises, finish the
exercises of Chapter 11.
Collegeweek 6 (week 42):
Wednesday October 19: Rest of Chapter 11 (Riemann vs. Lebesgue
integrals)+ begin of Chapter 12. Exercises: finish the exercises of
Chapter 11
Friday October 21:Chapter 12. Exercises:
p. 117: 1, 4, 6, 7, 8, 10, 15, 21.
Hand in Exercise due
date Friday October 28 during the exercise hour.
Collegeweek 7 (week 43):
Wednesday October 26: Rest of Chapter 12+Chapter 13. Exercises p.
130: 1, 2, 4, 6, 7, 8(i), 9, 11, 12.
Friday October 28: Chapter of 13 + begin Chapter 16 (till page 169).
Exercises p. 173: 1, 2, 3, 4, 5, 7(i, ii), 10. For students
eligible for the reparation Quiz go to room BBL165 during the
exercise
hour.
Hand in Exercise
date November 4 during the
exercise hour.
Collegeweek 8 (week 44):
Wednesday November 2: Finish Chapter 16. Exercises: finish all the
exercises of the previous weeks
Friday November 4: Finish whatever is left of Chapter 16. Exercises:
do practice exams.
Collegeweek 9 (week 45): Final exam Wednesday 09/11/2016
from 16:00-19:00 in EDUC (THEATRON)
Open
book exam, but you are only allowed to use the book of R.
Schilling,
Measures, Integrals and Martingales).