Measure and Integration 2015-16
Lecturer: Karma Dajani
Student assistents: Lars van den Berg (l.j.vandenberg@students.uu.nl) en Pol van Hoften (p.vanhoften@uu.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 161 and Exercises 15.15-17.00 in BBG 169.
Friday: Lecture 11.00-12.45 in BBG 161 and Exercises 13.15-15.00 in rin BBG 161.
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 October 14 (Chapters 3-9).
Open book exam, but you are only allowed to use the book of R. Schilling, Measures, Integrals and Martingales).
-- Final exam: Friday 06/11/2015 from 13:30-16:30 in Beatrix (6th floor)
-- Hertentamen: Wednesday 23/12/2015 from 13:30-16:30 in BBG 201
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 9: Chapter 3--Exercises p.20: 1, 2, 4, 8, 9, 11, 12.
Friday September 11: Chapter 4--Exercises p.28: 4, 5, 6, 8, 10, 11, 13.
Hand-in Exercise 1 due date Friday September 18.
Collegeweek 2 (week 38):
Wednesday September 16: Chapter 5. Exercises p.36: 2,4,5,7,8,9,10.
Friday September 18: Chapter 6. Exercises p.46: 3,4,5,7,8,9.
Hand-in exercise 2 due date Friday September 25.
Collegeweek 3 (week 39):
Wednesday September 23: Chapter 7. Exercises p.54: 1,3,6,8,4,5,7,10 (work out the exercises in the given order).
Friday September 25: Chapter 8. Exercises p.66: 2, 3, 4, 5, 6 ,9, 12, 15.
Hand in exercise 3 due date Friday October 2 (to be handed in during the exercise class).
Collegeweek 4 (week 40):
Wednesday September 30: Chapter 9. Exercises p.73: 1,5,6,7,8,9,10.
Friday October 2: Chapter 10. Exercises p.84: 2,3,5((i)-(iv)),7,9.
Hand in exercise
Due date Friday Friday October 9 during the Exercise hour.
Collegeweek 5 (week 41):
Wednesday October 7: Chapter 11. Exercises p.101: 1, 4, 6, 7, 8, 12, 15 (assume that X is non-negative), 16.
Friday October 9: Chapter 12. Exercises p. 117: 1, 6, 7, 8, 10, 15, 21.
Hand-in exercise due date October 16 (to be handed in during the exercise class).
Collegeweek 6 (week 42):
Wednesday October 14: Quiz from 13:15-15:00 (during the lecture 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).
No new exercises, finish the exercises of Chapters 11 and 12.
Friday October 16: Chapter 13. Exercises p. 130: 1, 2, 4, 6, 7, 8(i), 9, 11, 12.
NO HAND-IN
Solutions Quiz
Collegeweek 7 (week 43):
Wednesday October 21: Chapter 16 (till page 169). Exercises p. 173: 1, 2, 3, 4, 5, 7(i, ii), 10.
Friday October 23: Radon-Nikodym Theorem, the lecture notes are chapters SignedMEasures.pdf
and RadonNikodym.pdf from the book of Richard Bass, Analysis for Graduate Students. Exercises RND.pdf Solutions
Hand-in Exercise Due date Friday October 30 during the Exercise hour.
Collegeweek 8 (week 44):
Wednesday October 28: No Lecture hour ONLY Exercise hour : Practice Exam. Solutions
Friday October 30: No Lecture Hour only Exercise Hour: another practice exam Solutions
Final Friday November 6 from 13:30-16:30 in Beatrix (6th floor). Open
book exam, but you are only allowed to use the book of R. Schilling,
Measures, Integrals and Martingales), and the extra notes on Radon
Nikodym and Signed Measures.