Link to KdVI


Measure Theoretic probability

Fall 2016


Sonja Cox

(Personal page UvA) (Home page)

Email: s.g.cox AT

Sonja Cox

Teaching assistants

From September 21st up to (and including) November 2nd:

Kirsten Wang ( AT

From November 3rd onwards:

Alisa Kirichenko (a.kirichenko AT



To provide an introduction to the basic notions and results of measure theory and how these are used in probability theory.


The course is essentially self-contained, but the measure-theoretical basics (sigma-algebra, measurable space, Dynkin's lemma, Caratheodory's extension theorem, measurable functions, Lebesgue measure and -integral) are explained only very briefly. A student who is unfamiliar with this concepts will need to invest some extra time to succesfully complete the course.

Lecture notes and other reading material

Lecture notes can be downloaded here and printed on demand e.g. from the UvA campusprint (you need to make an account first). For students with UvA NetID: order the lecture notes at The lecture notes were written by Peter Spreij. Recommended additional reading material (if you are having difficulties with the lecture notes, perhaps because you are not familiar with measure theory):

Exercise classes, miniprojects, and homework

The schedule for the homework assignments can be found below (exercises are in lecture notes). (Part of) the homework will be graded, the average grade may raise (but not lower) the final grade. See also Exam below.

A bonus on the exam can be earned by presenting one part of these miniprojects in the exercise class. Sign up for a miniproject in class or by mailing one of the teaching assistants. You will get a grade for your presentation (integer between 0 and 6) that will count as a bonus for your final grade. See also Exam below. Details will be explained in the first lecture.

Schedule 2016

Lecture date Material covered Presenting students Exercises assigned Exercises due on Solutions
14-09 Ch. 1 Not applicable 1.1, 1.6, 1.11 21-09 (14:00) Solutions
21-09 Sec. 3.1, 3.2, 3.3 Fabian, and Jolien (UvA) 2.6, 3.10, 3.12 (typo in 3.10 regarding calligraphic F, see link.) 28-09 (14:00) Solutions
28-09 Sec. 4.1, 4.2 Mark vd B., Lianne vd V. (UL), Benthen Z. 4.2, 4.6, 4.7 05-10 (14:00) Solutions
05-10 Sec. 4.3, 4.4, 4.7 S. Franssen, L. Maxim 4.9, 4.10, 4.11 12-10 (14:00) Solutions
12-10 Sec. 5.1, 5.2 Wessel M., Bastiaan F., Abdel B.(UvA?) 5.2, 5.4, and read appendix A. 19-10 (14:00) Solutions
19-10 Sec. 6.1, 6.2, 6.3 Gideon J., Ismani N., Sjoerd J.(UvA) 6.4, 6.5, 6.9 26-10 (14:00) Solutions
26-10 Sec. 8.1 Wen W., Dechao W.(UvA) 8.2, 8.3, 8.9 02-11 (14:00) Solutions
02-11 Sec. 9.1, 9.2 Just B., Javier S., Dafni M. 9.4, 9.6, 9.8 (read Thm 9.15), 9.9 09-11 (14:00) Solutions
09-11 Sec. 9.3, 9.4, 10.1 Ardjen P., Daphne v L., Hamza A. 9.10, 9.14, 10.5 16-11 (14:00) Solutions
16-11 7.2, 10.2 Joost O., Hui Z., Audrius J. 7.14, 10.7, 10.8. 23-11 (14:00) Solutions
23-11 10.4, Def. 12.1, Prop. 12.2, Cor. 12.5 Jens K., Tammo H., Muriel P. 10.11, 12.1, 12.4 30-11 (14:00) Solutions
30-11 12.2 Bert t B., Rens K., Machiel Telling 12.11, 12.12 07-12 (14:00) Solutions
07-12 13.1, 13.2 Giovanni P., Camilla T., Caroline U. 13.8, 13.9 14-12 (14:00) Solutions
14-12 14.5, exam 2015, resit 2015, last year's exam and last year's resit Marieke vd W., Sophie H., Jori H., Shahzeb, Jules C., Rajesh M., Mathijs de L. Jurriaan P. No homework
January 9th, 15:00-17:00, G2.10, January 27th, 13:00-15:00, G3.10 Questions regarding the exam

)* Tentative program, will be updated after the lecture.


The list of `intended learning outcomes' (i.e., what you need to be able to do at the exam) can be found here (same list as in announcements). The course provides the necessary background for follow up courses like Stochastic Processes, Stochastic Differential Equations and Stochastic Integration.

Reimbursement of travel costs

See here.


At the end of the course there will be a written examination (for details, see announcements).

The final mark (F) is determined as

F = min( 10, max(E, 1/3 * H + 2/3 * E) + B/10 ),

where E is the grade obtained on the final exam, H is the average grade obtained for the homework, and B in {0,1,2,4,5,6} is the bonus that can be obtained by presenting a miniproject during the exercise class.