Measure and Integration
Module MA2003
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 SS 2012
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
| available module versions | |
|---|---|
| WS 2012/3 | SS 2012 |
Basic Information
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
Content
sigma algebra, measure, Borel sigma algebra, Lebesgue measure,
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)
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)
Learning Outcome
Having completed the course with success, the student is able to handle with confidence the Lebesgue integral in a general measure theoretic context and with respect to its fundamental convergence properties.
Preconditions
MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra and Discrete Structures 1, MA1102 Linear Algebra and Discrete Structures 2
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
| Type | SWS | Title | Lecturer(s) | Dates |
|---|---|---|---|---|
| VO | 2 | Measure and Integration Theory | Bornemann, F. Ludwig, C. |
Mon, 14:00–16:00, Interims I 102 and singular or moved dates |
| UE | 1 | Measure and Integration Theory (Exercise Session) | Bornemann, F. Ludwig, C. | dates in groups |
Learning and Teaching Methods
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should animate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. At the beginning of the module, the practice sessions will be offered under guidance, but during the term the sessions will become more independent, and intensify learning individually as well as in small groups.
Media
blackboard
Literature
D. Werner, Kapitel IV aus: Einführung in die höhere Analysis. Springer, 2006.
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.
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.
Module Exam
Description of exams and course work
The module examination is based on a written exam (60 minutes). Students have to deal with Lebesgue integrals in a general measure theoretical context adequately and determine the basic convergence properties.
Exam Repetition
The exam may be repeated at the end of the semester.