*Course Syllabus for*
# Specialised Course on Integration Theory

Fördjupningskurs till integrationsteori

## MATP29F, 7.5 credits

**Valid from:** Autumn 2018

**Decided by:** Professor Thomas Johansson

**Date of establishment:** 2018-08-24

## General Information

**Division:** Mathematics

**Course type:** Course given jointly for second and third cycle

**The course is also given at second-cycle level with course code:** MATP29

**Teaching language:** English

## Aim

The aim of the course is to the postgraduate student knowledge about mathematical measure theory. This is important for research within mathematical analysis, probability theory and mathematical physics.

## Goals

*Knowledge and Understanding*

For a passing grade the doctoral student must

- be able to explain important concepts, such as finite measure, absolutely continuous measure and singular measure.
- be able to give examples of how measure theory is used within other branches of mathematics.

*Competences and Skills*

For a passing grade the doctoral student must
be able to formulate and prove the main theorems of the course.

## Course Contents

The course covers fundamental theorems, such as the Radon-Nikodym theorem, and Lebesgue's decomposition, and basic theory of Lebesgue-Stieltjes integration.

## Course Literature

Cohn, Donald L.: Measure Theory: Second Edition. Birkhäuser, 2013. ISBN 9781461469551.

**Types of instruction:** Lectures, seminars

**Examination formats:** Written exam, oral exam, written assignments

**Grading scale:** Failed, pass

**Examiner:**

## Admission Details

**Assumed prior knowledge:** For admission to the course, at least 67.5 credits in mathematics are required, in which should be included the course MATM19 Integration theory, 7.5 credits, or equivalent and English B or equivalent.

## Course Occasion Information

**Course coordinators:**

**Web page:** https://liveatlund.lu.se/departments/Mathnfak/MATP29/Pages/default.aspx