Measure and Integration 2014-15

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 room HFG (wisk) 611 and Exercises 15.15-17.00 in room HFG (wisk) 611.

Friday: Lecture 11.00-12.45 in room HFG (wisk) 611 and Exercises 13.15-15.00 in room HFG (wisk) 611.

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 December 10 from 13:15-15:00 (during the lecture 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: Wednesday 28-01-2015 from 13:30-16:30 in Ruppert Wit.

-- Hertentamen: Wednesday March 11 from 13:30-16:30 in BBG 079.

Grades: Final grade=0.2H+0.3Q+0.5F (Q=quiz grade, F=final exam grade, H=hand-in exercises).

Announcements:  No classes on Friday December 17.

Material covered/to be covered:


Collegeweek 1 (week 46):

Wednesday November 12 : Chapter 3--Exercises p.20: 1, 2, 4, 8, 9, 11, 12.  Solutions

Friday November 14: Chapter 4--Exercises p.28: 4, 5, 6, 8, 10, 11, 13. Solutions

Hand in  due date Friday November 21 (to be handed in during the exercise class).


Collegeweek 2 (week 47):

Wednesday November 19: Chapter 5. Exercises  p.36: 2,4,5,7,8,9,10. Solutions
Friday November 21: Chapter 6. Exercises p.46: 3,4,5,7,8,9. Solutions

Hand in exercise    due date Friday November 28 (to be handed in during the exercise class).


Collegeweek 3 (week 48):

Wednesday February 26: Chapter 7. Exercises  p.54: 1,3,6,8,4,5,7,10 (work out the exercises in the given order). Solutions
Friday February 28: Chapter 8. Exercises p.66: 2, 3, 4, 5, 6 ,9, 12, 15. Solutions
Hand in exercise   due date Friday December 5 (to be handed in during the exercise class).


Collegeweek 4 (week 49):
Wednesday December 3: Chapter 9. Exercises p.73: 1,5,6,7,8,9,10. Solutions
Friday December 5: Chapter 10. Exercises p.84: 2,3,5((i)-(iv)),7,9. Solutions
Hand in exercise due date Wednesday December 17.  (to be handed in during the exercise class).

Collegeweek 5 (week 50):
Wednesday December 10: 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 Chapter 10.
Friday December 12: No Classes (both lecture and exercise hour).
NO HAND-IN EXERCISE.

Collegeweek 6 (week 51):
Wednesday December 17:  Chapter 11. Exercises p.101: 1, 4, 6, 7, 8, 12, 15 (assume that X is non-negative), 16. Solutions
Friday December 19: Chapter 12. Exercises p. 117: 1, 6, 7, 8, 10, 15, 21. Solutions
Hand-in .
due date Friday January 9  (to be handed in during the exercise class).

Collegeweek 7(week 52) + Collegeweek 8(week 1): NO CLASSES (Hertentamen week+ Kerstvakantie)



Collegeweek 8 (week2):

Wednesday January 7:  Chapter 13. Exercises p. 130: 1, 2,  4,  6, 7, 8(i), 9, 11, 12.  Solutions Solutions
Friday January 9: Rest of Chapter 13 + Chapter 16 (till page 169). Exercises p. 173: 1, 2, 3, 4, 5, 7(i, ii), 10.

Hand-in exercise  due date Friday January 16  (to be handed in during the exercise class).



Collegeweek 9 (week3):

Wednesday January 14:  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
Friday January 16:  Rest of Radon-Nikodym Theorem. No New Exercises, finish all the exercises from past weeks. You can also start working on the Practice Final. Solutions
No Hand-in exercise

Collegeweek 10 (week4):

Wednesday January 21:  Practice Final Exercises see attachment of last week and here some extra practice ExtraPracticeMI2014-15.pdf
Solutions

Friday January 23: No Lecture hour, but there is an exercise hour from 13:15-15:00.

Final exam: Wednesday 28-01-2015 from 13:30-16:30 in Ruppert Wit. 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.
Hertentamen: Wednesday March 11 from 13:30-16:30 in BBG 079. 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.