Theory of Measure and Integration
Objectives and Content
Contents are the Lebesgue integral, general theory of measure spaces and measurable functions, Lebesgue-Stieltjes measure on the real line, the Radon-Nikodym theorem, Fubinis theorem, Lp-spaces and related topics.
After completed course, the students are expected to be able to:
- Describe basic properties of sigma-algebras and the Lebesgue integral
- Explain the construction of the Lebesgue measure on Euclidean space
- Describe the relationship between continous functions and general integrable functions
- Work with Lebesgue-Stieltjes integral on the real line.
- Determine questions related to different kinds of convergence, like Lp-convergence, convergence in measure and convergence almost everywhere
- describe the main ideas of the proofs for the Fubini-and Radon-Nikodym theorem.
Recommended Previous Knowledge
Credit Reduction due to Course Overlap
M212: 10 ECTS
Forms of Assessment
Available aids: None
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.