Math 205A : Syllabus

Here is a week-by-week syllabus (changes are possible, and the content will be adapted to the needs of the course).

Sep 24, 26

sigma-algebras, measure and probability spaces, generated sigma-algebras. Caratheodory extension theorem (statement and proof outline).

Oct 1, Oct 3

Finishing proof of Caratheodory extension theorem. Application to Lebesgue measure. Completeness and regularity.

Oct 8, 10

Measurable functions and their integral. Almost sure convergence. Monotone convergence theorem, dominated convergence theorem.

Oct 15, 17

Convergence of measurable functions, Lp spaces.

Oct 22, 25

Hahn decomposition, Radon-Nikodym theorem.

Oct 29, 31

Continuing Radon-Nikodym. Differentiation.

Nov 5, 7

Product meassures and Fubini's theorem.

Nov 12, 14

Riesz representation theorem.

Nov 19, 21

To be defined

Dec 3, 5

Review.

Homeworks will be assigned every Thursday, the first time on September 25, and due the following Thursday (a total of 9 homeworks will be assigned).

An in-class midterm will be given on Tuesday, October 22, during normal class times. You are allowed to bring and consult the listed textbooks (Billingsley, Cohn), but no other sources.

Stanford is committed to providing equal educational opportunities for disabled students. Disabled students are a valued and essential part of the Stanford community. We welcome you to our class. If you experience disability, please register with the Office of Accessible Education (OAE). Professional staff will evaluate your needs, support appropriate and reasonable accommodations, and prepare an Academic Accommodation Letter for faculty. To get started, or to re-initiate services, please visit this address.

If you already have an Academic Accommodation Letter, please use the googleform tinyurl address https:goto.stanford.edu/math21oae (where 21 is your course number, you need to change it to your own course number 53, 61cm, 104, 171, 210a, etc) to upload it and detail the specific accommodations you will need in this course. Letters are preferred by the end of week 2, and at least two weeks in advance of any exam, so we may partner with you and OAE to identify any barriers to access and inclusion that might be encountered in your experience of this course. New accommodation letters, or revised letters, are welcome throughout the quarter; please note that there may be constraints in fulfilling last-minute requests.