Groups are selected in myStudies. Einige Übungsgruppen werden auf Deutsch gehalten. Some exercise classes will be held in English. Für die Übungen vom 4. März 2020 siehe Link
Introduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces
Objective
Basic acquaintance with the abstract theory of measure and integration
Content
Introduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces
Lecture notes
New lecture notes in English will be made available during the course
Literature
1. L. Evans and R.F. Gariepy " Measure theory and fine properties of functions" 2. Walter Rudin "Real and complex analysis" 3. R. Bartle The elements of Integration and Lebesgue Measure 4. The notes by Prof. Michael Struwe Springsemester 2013, Link. 5. The notes by Prof. UrsLang Springsemester 2019. Link 6. P. Cannarsa & T. D'Aprile: Lecture notes on Measure Theory and Functional Analysis: Link .
Performance assessment
Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
In examination block for
Bachelor's Degree Programme in Mathematics 2016; Version 25.02.2020 (Examination Block 2) Bachelor's Programme in Mathematics 2010; Version 24.02.2016 (Examination Block 2)
The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examination
oral 20 minutes
Additional information on mode of examination
Die mündliche Prüfung kann auf Wunsch der Studierenden auch auf Deutsch abgelegt werden.
If the course unit is part of an examination block, the credits are allocated for the successful completion of the whole block. This information can be updated until the beginning of the semester; information on the examination timetable is binding.