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German original

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,
workload		 Lecture (2 SWS), recitation class (2 SWS) oder lecture (3 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 CP
Translation missing. German original:
Studienleistung: Erreichen von mindestens 50 Prozent der Punkte aus den wöchentlich zu bearbeitenden Übungsaufgaben.
Prüfungsleistung: Klausur oder mündliche Prüfung
Language,
Grading		 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
Duration,
frequency		 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

Contents

Measure theory

  • Set systems, functions on sets, measures
  • Extension of a measure according to Carathéodory
  • Lebesgue measure on R^n
  • Probability distributions on R

Integration theory

  • Measurable maps
  • Integration with respect to general measures
  • Convergence theorems
  • Product measures, Fubini's Theorem
  • The Banach space L_1

Qualification Goals

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.

Prerequisites

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den mathematischen Basismodulen Lineare Algebra und Analysis vermittelt werden.


Recommended Reading

  • Elstrodt, J.: Maß- und Integrationstheorie, Springer 1996.



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2018/19. 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:

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.