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401-2283-00L 6 Credits BSC D-PHYS , D-MATH
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Analysis III (Measure Theory)

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

Last Updated: 2026-06-01 11:31:23

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

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

Learning Materials (Links)

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)
  • Wed 15:15-16:00 (HG G 5)
  • Fri 10:15-12:00 (HG G 3)
3 h weekly
exercise Analysis III (Measure Theory)
ACHTUNG: Die beiden deutschsprachigen Übungsgruppen G-02 und G-03 (nicht aber G-01) finden am 6. Oktober im ML F 39 (anstatt im ML F 40 bzw. LEE D 101) statt.
  • Mon 16:15-18:00 (CHN G 42)
  • Mon 16:15-18:00 (LEE D 101)
  • Mon 16:15-18:00 (LFW C 5)
  • Mon 16:15-18:00 (ML F 40)
  • Mon 16:15-18:00 (ML H 41.1)
  • 06.10 Date 16:15-18:00 (ML F 39)
2 h weekly

Offered In