MATM39 Integration Theory, 7.5 credits, is an alternative-compulsory course at advanced level for a Master of Science degree in Mathematics. The course can be taken as an stand-alone course. The course is given at half-study pace during the first half of the autumn semester. The language of instruction is English.

Course Content
The Riemann integral taught in our beginner courses has the advantage that it is quite easy to define and in many cases easy to compute. At the same time there are many relatively simple functions which are not integrable in this sense, and the integral is quite unstable with respect to pointwise convergent sequences of integrable functions. In this course we present H. Lebesgue's extension of the Riemann integral in the most general context. One major advantage offered by the general approach is that it pertains also to the basics of Probability Theory. The course starts with sigma-algebras and measures on general sets, and the construction of measures based on outer measures. With these notions at hand, it turns to the definition of the integral, examples on the real line like the Lebesgue and Lebesgue-Stieltjes integrals, the Lebesgue integral in higher dimensions, convergence theorems, L^p-spaces, iterated integrals and the theorems of Fubini and Tonelli.

Teaching
The teaching consists of lectures and seminars.

Assessment
The examination consists of a written examination (5 credits) and an oral examination (2.5 credits) at the end of the course. The oral examination may only be taken by those students who passed the written examination.

More information regarding the examination as well as past examination problems can be found on the link below:

Regarding examination

Course Literature

Donald L. Cohn, Measure Theory, 2nd ed, 2013, ISBN: 978-1-4614-6955-1.
recommended complementary reading: Stein and Shakarachi; Real Analysis

Official Course Description

Course Evaluation
Link to course evaluations on the department's website:

Course Evaluations, Mathematics at Faculty of Science