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.

Instruction Details

Types of instruction: Lectures, seminars

Examination Details

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

Contact and Other Information

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