Measure and Integration Theory I
5 credits
Syllabus, Master's level, 1MA049
This course has been discontinued.
A revised version of the syllabus is available.
- Code
- 1MA049
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 23 April 2013
- Responsible department
- Department of Mathematics
Entry requirements
120 credit points including at least 90 credit points Mathematics
Learning outcomes
In order to pass the course (grade 3) the student should be able to
- use the measurability concept for functions and sets;
- use the -almost everywhere- concept;
- give an account of the construction of the Lebesgue integral and be able to use it;
- use the theorems about monotone and dominated convergence, and Fatou's lemma;
- describe the construction of product measures;
- use Fubini's theorem;
Content
Sigma algebras. Measure and exterior measure. Lebesgue measure in one and several dimensions. Measurability of functions. The Lebesgue integral and its relation to the Riemann integral. Product measures and Fubini's theorem.
Instruction
Lectures and problem solving sessions.
Assessment
Written examination at the end of the course combined with assignments given during the course.