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401-2284-00L 6 Credits BSC , MSC D-PHYS , D-MATH
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Measure and Integration

Mass und Integral

Lecturers & Examiners: Prof. Dr. Francesca Da Lio
VVZ CR n/a

Last Updated: 2026-02-05 15:54:17

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

Resources

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, https://people.math.ethz.ch/~struwe/Skripten/AnalysisIII-FS2013-12-9-13.pdf . 5. The notes by Prof. UrsLang Springsemester 2019. https://people.math.ethz.ch/~lang/mi.pdf 6. P. Cannarsa & T. D'Aprile: Lecture notes on Measure Theory and Functional Analysis: http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf .

Learning Materials (Links)

General Information

Language
English (lecture), German (exercise)
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 20 minutes
Die mündliche Prüfung kann auf Wunsch der Studierenden auch auf Deutsch abgelegt werden.

Course Components

Type Title Time & Place Hours
lecture Mass und Integral (Measure and Integration)
At least in February and March online via Zoom.
  • Wed 09:15-10:00 (HG F 3)
  • Fri 10:15-12:00 (HG F 3)
3 h weekly
exercise Mass und Integral
Groups are selected in myStudies. Einige Übungsgruppen werden auf Deutsch gehalten. Some exercise classes will be held in English. Zumindest im Februar und März online via Zoom. At least in February and March online via Zoom.
  • Wed 10:15-12:00 (HG E 33.5)
  • Wed 10:15-12:00 (HG G 26.1)
  • Wed 10:15-12:00 (LEE D 105)
  • Wed 10:15-12:00 (ML F 40)
  • Wed 10:15-12:00 (ML H 43)
  • Wed 10:15-12:00 (ML J 34.1)
2 h weekly

Offered In