Theory of Measure and Integration

Teaching semester

Irregular

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.

Recommended Previous Knowledge

MAT211

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.