## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-12-28-K-3

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 4.5 CP 93 h
2 V Lecture 28 h
1 U Exercise class (in small groups) 14 h
(2V+1U) 4.5 CP 42 h 93 h

## Basedata

SWS 2V+1U 4.5 CP = 135 h 1 Sem. in SuSe [3] Bachelor (Core) [DE] German Grothaus, Martin, Prof. Dr. (PROF | DEPT: MAT) Hussein, Amru, Jun. Prof. Dr. (PROF | DEPT: MAT) Korn, Ralf, Prof. Dr. (PROF | DEPT: MAT) Redenbach, Claudia, Prof. Dr. (PROF | DEPT: MAT) Ritter, Klaus, Prof. Dr. (PROF | DEPT: MAT) Sass, Jörn, Prof. Dr. (PROF | DEPT: MAT) [MAT-GRU] Mathematics (B.Sc. year 1 and 2) [NORM] Active

## 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.

## Contents

• 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,

## 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.

## Literature

• J. Elstrodt: Maß- und Integrationstheorie,
• H. Bauer: Maß- und Integrationstheorie.

## Materials

Further literature will be announced in the lecture(s); exercise material is provided.

## Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

None

## References to Course [MAT-12-28-K-3]

Module Name Context
[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
Course-Pool Name
[MAT-10-KPOOL-3] Pure Mathematics (B.Sc. Mathematics)