Part I, Integration theory

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

Lectures 1-7 ( Tuesdays): Kristian Bjerklöv. 

Exercise sessions: (Fridays): 

 

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. Recommended problems: 1.1: 2,3,4,6,7; 1.2: 2,3,6.

Lecture 2: Chapters 1.3-1.6. Recommended problems: 1.3: 1,2; 1.4: 4; 1.6: 3,4,5.

Lecture 3: Chapters 2.1-2.4. Recommended problems: 2.1: 6,9,10; 2.2: 2,3; 2.3: 2; 2.4: 3.

Lecture 4: Chapters 2.5-2.7. Recommended problems: 2.5: 2; 2.6: 3,4; 2.7: 3

Lecture 5: Chapters 2.8-2.11. Recommended problems: 2.8: 1; 2.9: 1; 2.10: 2,11,12,14.

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

Lecture 7: Chapters 2.14--2.16. Recommended problems: 2.14: 8; 2.16: 1,2,5

 

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 under Assignments in the left column (one week before the due date).

Assignment 1: Due September 20. You find Homework assignment 1 under "Assignments" in the left column.

Assignment 2: Due October 11.

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.