Theory of Measure and Integration

Postgraduate course

Course description

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.

Learning Outcomes

Learning outcomes

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 continuous 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.

Semester of Instruction

Irregular, course will be offered if it is on this course list: Workbook: Emneliste for innreisende utvekslingsstudenter (
Recommended Previous Knowledge
Credit Reduction due to Course Overlap
M212: 10 ECTS
Forms of Assessment

Oral examination

Available aids: None

Grading Scale
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.