# Measure theory

Course Code : | 1000WETMAT |

Study domain: | Mathematics |

Academic year: | 2017-2018 |

Semester: | 1st semester |

Sequentiality: | |

Contact hours: | 45 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 1st semester |

Lecturer(s) | Ben Berckmoes |

### 1. Prerequisites *

At the start of this course the student should have acquired the following competences:

an active knowledge of

an active knowledge of

- Dutch

The student has a strong background in set theory, general topology, linear algebra, and real analysis.

### 2. Learning outcomes *

- The student masters the language of measure theory.

### 3. Course contents *

The following topics will be covered:

- The Lebesgue measure

- The Lebesgue integral

- The Vitali, Lebesgue, and Fatou convergence theorems

- The monotone convergence theorem

- Basic L^p theory

- The Hölder, Cauchy-Schwarz, Lyapunov, and Minkowski inequalities

- Fubini’s theorem

- Applications in probability theory: independence and conditional expecations

### 4 International dimension*

### 5. Teaching method and planned learning activities

Class contact teachingLectures Practice sessions

### 6. Assessment method and criteria

ExaminationWritten with oral presentation Closed book Open-question

### 7. Study material *

#### 7.1 Required reading

Lecture notes will be made available.

**7.2 Optional reading**

The following study material can be studied voluntarily :### 8. Contact information *

ben.berckmoes@uantwerpen.be