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401-2465-AAL 12 Credits MSC D-MATH
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Analysis III and IV (Measure Theory / Fourier Theory and Hilbert Spaces)

Lecturers & Examiners: Prof. Dr. Francesca Da Lio, Prof. Dr. Mikaela Iacobelli
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
VVZ CR n/a

Last Updated: 2026-02-05 16:37:22

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

Die Vorlesung folgt dem Skript von der Dozentin(https://people.math.ethz.ch/~fdalio/Measuremainfile.pdf)

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
MSC
Frequency
Semesterly recurring

Examination

Type
session examination
Mode
written 180 minutes
Aids
None

Course Components

Type Title Time & Place Hours
revision course / private study Analysis III and IV (Measure Theory / Fourier Theory and Hilbert Spaces)
Self-study course. No presence required.
No time listed 360 h semesterly

Offered In