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Measure and Integration Theory
(dt. Maß- und Integrationstheorie)

Level, degree of commitment Advanced module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (2 SWS), recitation class (2 SWS) or lecture using videos (3 SWS), Repetitorium (2 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination (individual examination)
Language,
Grading		 German/English,
The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Business Mathematics.
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

  • Quantity systems, quantity functions, measures
  • Measure expansion according to Carathéodory
  • Lebesgu measure in R^n
  • Probability distributions on R

Integration theory

  • Measurable mappings
  • Integration with respect to general measures
  • Convergence Theorems
  • The L_p spaces
  • Product measures, theorem of Fubini
  • Measures with densities and the Radon-Nikodým theorem
  • The transformation formula
  • Absolute functions and the main theorem of differential and integral calculus

Qualification Goals

The students

  • are familiar with an abstract concept of measure and integration, which is necessary as a basis for advanced study of stochastics and calculus,
  • have practiced mathematical ways of working (developing mathematical intuition and its formal justification, abstraction, proof),
  • have improved their oral communication skills in exercises by practicing free speech in front of an audience and in discussion.

Prerequisites

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.


Applicability

Module imported from B.Sc. Business Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Data Science
  • M.Sc. Computer Science
  • LAaG Mathematics
  • BA Minor Mathematics

When studying M.Sc. Data Science, this module can be attended in the study area Free Compulsory Elective Modules.

The module is assigned to Mathematics. Further information on eligibility can be found in the description of the study area.


Recommended Reading

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



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. 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.