Valid from: Autumn 2018
Decided by: Professor Thomas Johansson
Date of establishment: 2018-08-24
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: MATM19
Teaching language: English
For many mathematical investigations the notion of integrability in the sense of Riemann, which is used in the basic courses, is insufficient. Above all, it is difficult to guarantee that the limit of a sequence of Riemann integrable functions is an integrable function. The aim of the course is to acquaint the postgraduate student with the Lebesgue integral, and important theorems valid for it. This theory is indispensable for researchers in, e.g., mathematical analysis, numerical analysis or stochastic processes.
Knowledge and Understanding
For a passing grade the doctoral student must be able to account for basic concepts and methods within theory of integration.
Competences and Skills
For a passing grade the doctoral student must
Basic theory of Lebesgue integration: basic measure theory, construction of the Lebesgue measure, convergence theorems and Fubini's theorem.
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
Admission requirements: At least 60 credits in mathematics as well as English B or
the equivalent are required.
Assumed prior knowledge: Calculus in one and several variables. Linear algebra.
Web page: https://liveatlund.lu.se/departments/Mathnfak/MATM19/Pages/default.aspx