401-2284-00L Measure and Integration
Semester | Spring Semester 2020 |
Lecturers | F. Da Lio |
Periodicity | yearly recurring course |
Language of instruction | English (lecture), German (exercise) |
Abstract | 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 . |