Measure and Integration Theory (2V+1U, 4.5 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|-||K||Lecture with exercise classes (V/U)||4.5 CP||93 h|
|1||U||Exercise class (in small groups)||14 h|
|(2V+1U)||4.5 CP||42 h||93 h|
|CP, Effort||4.5 CP = 135 h|
|Position of the semester||1 Sem. in SuSe|
|Level|| Bachelor (Core)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-GRU] Mathematics (B.Sc. year 1 and 2)|
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
- Examination number (Study achievement): 83155 ("Exercise Class Measure and Integration Theory")
- Details of the examination (type, duration, criteria) will be announced at the beginning of the course.
- systems of sets, Caratheodory theorem,
- d-dimensional Lebesgue measure,
- measurable functions, integral w.r.t. a measure, convergence theorems,
- Lp spaces,
- product measures, Fubini's theorem,
- transformation theorem,
- theorem of Radon-Nikodym.
Competencies / intended learning achievements
The students know the basic concepts, constructions, results and methods of proof of measure and integration theory. The content of the course is the basis for all advanced courses in stochastics and functional analysis.
- J. Elstrodt: Maß- und Integrationstheorie,
- H. Bauer: Maß- und Integrationstheorie.
Further literature will be announced in the lecture(s); exercise material is provided.
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
Requirements for attendance (formal)
References to Course [MAT-12-28-K-3]
|[MAT-12-10P-M-3]||Build-Up Module Mathematics (for Students of Physics)||WP: Obligation to choose||2V+1U, 5.0 LP|
|[MAT-12-20L_ERW-M-3]||Topic Module A: Mathematics in the Interplay between Abstraction and Concretisation||WP: Obligation to choose||2V+1U, 4.5 LP|
|[MAT-12-20L-M-3]||Topic Module A: Mathematics in the Interplay between Abstraction and Concretisation||WP: Obligation to choose||2V+1U, 4.5 LP|
|[MAT-12-2-M-3]||Measure Theory and Differential Equations||P: Obligatory||2V+1U, 4.5 LP|
|[MAT-10-KPOOL-3]||Pure Mathematics (B.Sc. Mathematics)|