250072 VO and 250069 PS Measure and Integration Theory.

Lecturer: Henk Bruin and Davide Ravotti

Please email Henk Bruin for more information on this course.

The proseminar will be given by Davide Ravotti.

Information from the Course catalogue and for the Proseminar.


No Exercise Class in the first week (October 7).


Day Time Room Type From To
Monday 8:00-9:30 HS2 Lecture3.10.202230.1.2023
Tuesday 8:00-9:30 HS2 Lecture4.10.202231.1.2023
Friday 8:00-8:45 SR10 Exercises14.10.202227.1.2023

Week 1 TypeTopic/Material
October 3Lecture: Bruin Introduction, Sigma-Algebras
October 4Lecture: Bruin
October 7Exercises: Ravotti No exercise class
Week 2 TypeTopic/Material
October 10Lecture: Ravotti Measures and outer measures,
measurable sets Bass Chapter 3 and 4.1
October 11Lecture: Ravotti
October 14Exercises: Ravotti Bass, Chapter 2, Exercises 1,2,3,5,7,9
Week 3 TypeTopic/Material
October 17Lecture: Bruin Lebesgue-Stieltjes measure and outer measure
Caratheodory extension theorem, Bass Chapter 4
October 18Lecture: Bruin
October 21Exercises: Ravotti Bass, Chapter 3, Exercises 2-7 and 9.
Week 4 TypeTopic/Material
October 24Lecture: Ravotti Measurable functions
Bass Chapter 5
October 25Lecture: Ravotti
October 28Exercises moved to Monday 31
Week 5 TypeTopic/Material
October 31Exercises: Bruin 8:45-9:30 Chapter 3: 4,5,6,7 and Chapter 4: 1,2
November 1No class All Saints Day
November 4Exercises: Ravotti Bass, Chapter 4, Exercises 4.6, 47, Chapter 5, 5.4, 5.5
Week 6 TypeTopic/Material
November 7Lecture: Bruin Lebesgue Density Theorem
November 8Lecture: Bruin Legesbue Integral
Bass Chapter 6
November 11Exercises: Ravotti Bass, Chapter 5, Exercises 5.1, 5.3, Chapter 6, 6.1 and 6.4
Week 7 TypeTopic/Material
November 14Lecture: Ravotti Limit Theorems
Bass, Chapter 7
November 15Lecture: Ravotti
November 18Exercises: Ravotti Exercises: 6.5 + three extra on the Lebesgue density theorem
Week 8 TypeTopic/Material
November 21Lecture: Bruin Properties for f = 0
Riemann integral
November 22Lecture: Bruin Chapter 8 and 9
November 25Exercises: Ravotti Exercises: 7.5, 7.10, 7.12, 7.17
Week 9 TypeTopic/Material
November 28Lecture: Ravotti Types of Convergence, Product measures
Chapter 10 + 11
November 29Lecture: Ravotti
December 2Exercises: Ravotti Exercises: 7.27, 8.2, 8.7, 8.8
Week 10 TypeTopic/Material
December 5Lecture: Ravotti Fubini's Theorem, Signed measures
Chapter 11 + 12
December 6Lecture: Bruin
December 9Exercises: Ravotti Exercises: 10.2, 10.4, 10.9, 11.4
Week 11 TypeTopic/Material
December 12Lecture: Bruin Jordan decomposition, absolute continuity,
Radon-Nikodym derivative
Chapter 12 + 13
December 13Lecture: Ravotti
December 16Exercises: Ravotti
Week 12 TypeTopic/Material
January 9Lecture:Ravotti Lp-spaces, Hölder and Minkovski inequality,
January 10Lecture:Ravotti
January 13Exercises: Ravotti
Week 13 TypeTopic/Material
January 16Lecture: Bruin Convolutions, bounded functional, Chapter 15
January 17Lecture: Bruin
January 20Exercises: Bruin Exercises 15.1, 15.6, 15.7 and the following: (a) Let f be the function on Rn defined by f(x) = e-1/(1-|x|^2) for |x|<1 and f(x) = 0 otherwise. Prove that f is infinitely differentiable on Rn. Is it real analytic?
Week 14 TypeTopic/Material
January 23Lecture:Bruin Riesz Representation Lemma, Chapter 17
January 24Lecture:Bruin
January 26Exercises: Ravotti


By oral examination on appointment.

References and resources

Updated August 2022