Measure and Integration
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Module version of WS 2020/1 (current)
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
|available module versions|
|WS 2020/1||SS 2020||WS 2012/3||SS 2012|
MA2003 is a semester module in German language at Bachelor’s level which is offered in winter semester.
This Module is included in the following catalogues within the study programs in physics.
- Further Modules from Other Disciplines
|Total workload||Contact hours||Credits (ECTS)|
|150 h||45 h||5 CP|
Content, Learning Outcome and Preconditions
integration theory in Rn based on the Lebesgue integral (including Fubini's theorem and transformation formula)
extension and uniqueness for sigma additive set functions (without proof)
measurable mappings, image measure, absolute continuity, density, general Lebesgue integral;
monotone and dominated convergence, Fatou's lemma, Lp spaces (including the Hölder and Minkowski inequalities, completeness)
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
Please keep in mind that course announcements are regularly only completed in the semester before.
|VO||2||Measure and Integration Theory||Bornemann, F. Ludwig, C.||
Mon, 14:00–16:00, Interims I 102
|UE||1||Measure and Integration Theory (Exercise Session)||Bornemann, F. Ludwig, C.||dates in groups||
Learning and Teaching Methods
E.H. Lieb, M. Loss, Chapter 1 and 2 from: Analysis. American Mathematical Society, 2nd edition, 2001.
M. Brokate, G. Kersting: Maß und Integral. Birkhäuser, 2010. English translation: Measure and integral. Birkhäuser, 2015.
Description of exams and course work
In dieser wird überprüft, inwieweit die Studierenden ein Lebesgue-Integral in einem allgemeinen maßtheoretischen Kontext sowie hinsichtlich seiner grundlegenden Konvergenzeigenschaften sicher handhaben können.
The exam may be repeated at the end of the semester.