Entry requirements

120 credits including at least 90 credits in mathematics. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

On completion of the course, 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.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.