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Analysis III (Measure Theory)
Last Updated: 2026-06-03 00:07:54
Abstract
Measure and Integration Theory, including: Caratheodory's Theorem, Lebesgue Measure, Radon Measure, Hausdorff Measure, Convergence Theorems, L^p Spaces, Radon-Nikodym Theorem, Product Measure and Fubini's Theorem
Objective
Basics of abstract measure and integration theory
Content
Measure Spaces (Lebesgue Measure, Hausdorff Measure, Radon Measure) • Measurable Functions: definition and properties • Integration: definition, properties, theorems of convergence, Lebesgue L^p spaces • Product Measures and Multiple Integrals. Fubini and Tonelli Theorems, Convolutions • Differentiation of measures (if time permits)
Resources
Lecture Notes
The lecture follows the professor's script.
Literature
1. Lecture notes by Professor Michael Struwe ( http://www.math.ethz.ch/~struwe/Skripten/AnalysisIII-SS2007-18-4-08.pdf ) 2. L. Evans and R.F. Gariepy "Measure theory and fine properties of functions" 3. Walter Rudin "Real and complex analysis" 4. R. Bartle The elements of Integration and Lebesgue Measure 5. P. Cannarsa & T. D'Aprile: Lecture notes on Measure Theory and Functional Analysis. http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf
General Information
- Language
- English
- Levels
- BSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
Analysis III (Measure Theory)
This course is offered in English in HS 2026.
No class on 23 September 2026 [to be confirmed]; make-up class planned to take place on Friday, 2 October 2026 12:15-13:00 [tbc].
|
No time listed | 3 h weekly |
| exercise |
Analysis III (Measure Theory)
One exercise group is conducted in German.
|
No time listed | 2 h weekly |