Mathematical Foundations of Probability theory

Lecturers and Seminarists

Lecturer	Vladimir Ulyanov	[]	T924
Seminarist	Samsonov Sergey	[svsamsonov@hse.ru]	T926

About the course

This page contains materials for the Mathematical Foundations of Probability theory course in 2022/2023, mandatory for 1st year Master students of the MML program (HSE and Skoltech).

Grading

The final grade consists of 2 components (each is non-negative real number from 0 to 10, without any intermediate rounding) :

• O_HW for the hometasks
• O_Exam for the final exam

The formula for the final grade is

• O_Final = 0.5*O_HW + 0.5*O_Exam

with the usual (arithmetical) rounding rule.

Table with grades

Lectures

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Seminars

• []

Homeworks

• [1] Homework #1, deadline: 16.10.2022, 23:59.
• [2] Homework #2, deadline: 29.10.2022, 23:59. Deadline was extended!

Exam

Exam will be organised on 29.10.2022. Please split into 2 groups: first group starts exam at 09:00, second group starts at 10:30. You can book am exam slot below. Exam question will contain 1 theoretical question and 1 problem. Using any materials, electronic devices is allowed during preparation, but not during the answer. The proofs that were not given in the lectures can be omitted.

• List of exam questions.
• link to exam slots
• exam problems

Recommended literature (1st term)

• https://59clc.files.wordpress.com/2012/05/paul_r-_halmos_measure_theory_graduate_texts_inbookfi-org.pdf - P. Halmos. Measure theory. Chapters 1-6;
• phys.nsu.ru/korobkov/Fudan_2018_Sobolev_Spaces/Measure-Theory-and-Fine-Properties-of-Functions-Revised-Edition.pdf - L. Evans. Measure theory and fine properties of functions. Chapter 1;
• https://diendantoanhoc.org/index.php?app=core&module=attach&section=attach&attach_id=12514 - V. Bogachev. Measure theory. Chapters 1,2.
• https://www.youtube.com/watch?v=KRtrdtUI9YQ&list=PLhe7c-LCgl4IVzTaYL8kC-exzBJiJms2B - CMC MSU lectures (in russian!)