Measure and Integration Theory
(dt. Maß- und Integrationstheorie)
|Level, degree of commitment in original study programme||Intermediate module, required module|
|Forms of teaching and learning,
|Lecture (2 SWS), recitation class (2 SWS) oder
lecture (3 SWS), recitation class (1 SWS), |
180 hours (60 h attendance, 120 h private study)
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
|German,The grading is done with 0 to 15 points according to the examination regulations for study course B.Sc. Business Mathematics.|
|Original study programme||B.Sc. Wirtschaftsmathematik / Grundlagen der Mathematik|
|One semester, |
each summer semester
|Person in charge of the module's outline||Prof. Dr. Ilka Agricola, Prof. Dr. Pablo Ramacher, Prof. Dr. Hajo Holzmann|
- Set systems, functions on sets, measures
- Extension of a measure according to Carathéodory
- Lebesgue measure on R^n
- Probability distributions on R
- Measurable maps
- Integration with respect to general measures
- Convergence theorems
- Product measures, Fubini's Theorem
- The Banach space L_1
The students shall
- learn the abstract concepts of measure and of integration, which are necessary as a basis for an advanced study of stochastics and analysis,
- practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
- improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussions.
None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis.
- Elstrodt, J.: Maß- und Integrationstheorie, Springer 1996.
This page describes a module according to the latest valid module guide in Wintersemester 2019/20. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:
- WiSe 2016/17 (no corresponding element)
- SoSe 2018 (no corresponding element)
- WiSe 2018/19
- WiSe 2019/20
- WiSe 2020/21
- SoSe 2021
- WiSe 2021/22
The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.
The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.