Part I, Integration theory

For Schedule, click here. Links to an external site.

Lectures 1-7 ( Tuesdays): Kristian Bjerklöv. Lectures via zoom. Link: https://kth-se.zoom.us/j/63921333002 Links to an external site.

Exercise sessions: (Fridays): Scott Mason. Via zoom. Link: https://kth-se.zoom.us/j/62493747119 Links to an external site.

 

Topics:

Basics of measure theory

Integration on measure spaces (Lebesgue integral)

Convergence theorems

Product measures, and Fubini's theorem

 Sections 1.1-1.6  (1.7) ;  2.1-2.11, 2.14-2.16 (in Friedman's book)

 

Preliminary planning of the lectures:

Lecture 1: Chapters 1.1-1.2 

Lecture 2: Chapters 1.3-1.5

Lecture 3: Chapters 1.6, 2.1-2.4

Lecture 4: Chapters 2.4, 2.5, 2.6, 2.7

Lecture 5: Chapters 2.7--2.11

Lecture 6, Application (Ergodic theory). Short notes.   Download Short notes.  

+ Lecture notes Download Lecture notes

Lecture 7: Chapters 2.14--2.16

 

Homework assignments

There will be two sets of homework assignments, each passed one giving 1 p for the final exam (to part A). The assignments will be posted here (one week before the due date).

Assignment 1: Due September 21. You find Homework assignment 1 under "Assignments" in the left column.

Assignment 2: Due October 12. You find Homework assignment 2 under "Assignments" in the left column.

The assessment of the homework assignements is as follows. On each (of the two) homework assignment ONE of the problems is randomly chosen. This (and only this) problem is graded (the same problem for all students). If this problem is correctly solved, with a complete solution, one gets 1p.

Solutions to the problems will be presented/discussed at the exercise sessions.