Course Code : | 1000WETMAT |

Study domain: | Mathematics |

Academic year: | 2019-2020 |

Semester: | 1st semester |

Sequentiality: | Min 8/20 : Calculus, Lineair algebra en geometry AND Probability theory AND min 8/20 all courses Ba1 MATH |

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) | Werner Peeters Wouter Van Den Haute |

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

an active knowledge of

an active knowledge of

- Dutch

The following course contents precede this course:

- The knowledge about set theory from Discrete mathematics
- The notions about metric and normed spaces and continuity from Multivariate calculus
- General topology

- The students know a large selection of relevant definitions from measure theory, as well as the implications between them
- The students can reproduce the proofs of all implications and equivalenes, and highlight their importance.
- The students know a large selection of relevant examples and counterexamples, and can test the properties of a given measure space.

The following topics will be covered:

- Measurable spaces
- Measure spaces
- De Borel sigma algebra and the Lebesgue measure on R^n
- Measurable and elementary mappings
- The Lebesgue integral
- The spaces L^p(Omega,A,mu)
- Convergence theorems
- Equi-integrability
- The Radon-Nikodym derivative
- Product measures
- Convolution of measures

Class contact teachingLectures Practice sessions

ExaminationWritten examination without oral presentation Oral with written preparation

W. Peeters. Maattheorie

P. Billingsley. Probability and measure - third edition. Wiley series in probability and mathematical

statistics. New York: John Wiley & Sons, 1995

A.N. Kolmogorov and S.V. Fomin. Measure, Lebesgue integrals, and Hilbert space. Academic Press,1961

dr Werner Peeters

Dept. Wiskunde

Campus Middelheim gebouw G lokaal G3.14

Tel. 03/265.32.93

E-mail: werner.peeters@uantwerpen.be

W. Van Den Haute

Dept. Wiskunde

Campus Middelheim gebouw G lokaal G2.28

Tel. 03/265.34.73

E-mail: wouter.vandenhaute@uantwerpen.be