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.
| Day | Time | Room | Type | From | To |
|---|---|---|---|---|---|
| Monday | 8:00-9:30 | HS2 | Lecture | 3.10.2022 | 30.1.2023 |
| Tuesday | 8:00-9:30 | HS2 | Lecture | 4.10.2022 | 31.1.2023 |
| Friday | 8:00-8:45 | SR10 | Exercises | 14.10.2022 | 27.1.2023 |
| Week 1 | Type | Topic/Material |
|---|---|---|
| October 3 | Lecture: Bruin | Introduction, Sigma-Algebras |
| October 4 | Lecture: Bruin | |
| October 7 | Exercises: Ravotti | No exercise class |
| Week 2 | Type | Topic/Material |
| October 10 | Lecture: Ravotti | Measures and outer measures, measurable sets Bass Chapter 3 and 4.1 |
| October 11 | Lecture: Ravotti | |
| October 14 | Exercises: Ravotti | Bass, Chapter 2, Exercises 1,2,3,5,7,9 |
| Week 3 | Type | Topic/Material |
| October 17 | Lecture: Bruin | Lebesgue-Stieltjes measure and outer measure Caratheodory extension theorem, Bass Chapter 4 |
| October 18 | Lecture: Bruin | |
| October 21 | Exercises: Ravotti | Bass, Chapter 3, Exercises 2-7 and 9. |
| Week 4 | Type | Topic/Material |
| October 24 | Lecture: Ravotti | Measurable functions Bass Chapter 5 |
| October 25 | Lecture: Ravotti | |
| October 28 | Exercises moved to Monday 31 | |
| Week 5 | Type | Topic/Material |
| October 31 | Exercises: Bruin 8:45-9:30 | Chapter 3: 4,5,6,7 and Chapter 4: 1,2 |
| November 1 | No class | All Saints Day |
| November 4 | Exercises: Ravotti | Bass, Chapter 4, Exercises 4.6, 47, Chapter 5, 5.4, 5.5 |
| Week 6 | Type | Topic/Material |
| November 7 | Lecture: Bruin | Lebesgue Density Theorem |
| November 8 | Lecture: Bruin | Legesbue Integral Bass Chapter 6 |
| November 11 | Exercises: Ravotti | Bass, Chapter 5, Exercises 5.1, 5.3, Chapter 6, 6.1 and 6.4 |
| Week 7 | Type | Topic/Material |
| November 14 | Lecture: Ravotti |
Limit Theorems Bass, Chapter 7 |
| November 15 | Lecture: Ravotti | |
| November 18 | Exercises: Ravotti | Exercises: 6.5 + three extra on the Lebesgue density theorem |
| Week 8 | Type | Topic/Material |
| November 21 | Lecture: Bruin |
Properties for f = 0 Riemann integral |
| November 22 | Lecture: Bruin | Chapter 8 and 9 |
| November 25 | Exercises: Ravotti | Exercises: 7.5, 7.10, 7.12, 7.17 |
| Week 9 | Type | Topic/Material |
| November 28 | Lecture: Ravotti |
Types of Convergence, Product measures Chapter 10 + 11 |
| November 29 | Lecture: Ravotti | |
| December 2 | Exercises: Ravotti | Exercises: 7.27, 8.2, 8.7, 8.8 |
| Week 10 | Type | Topic/Material |
| December 5 | Lecture: Ravotti |
Fubini's Theorem, Signed measures Chapter 11 + 12 |
| December 6 | Lecture: Bruin | |
| December 9 | Exercises: Ravotti | Exercises: 10.2, 10.4, 10.9, 11.4 |
| Week 11 | Type | Topic/Material |
| December 12 | Lecture: Bruin |
Jordan decomposition, absolute continuity, Radon-Nikodym derivative Chapter 12 + 13 |
| December 13 | Lecture: Ravotti | |
| December 16 | Exercises: Ravotti | |
| Week 12 | Type | Topic/Material |
| January 9 | Lecture:Ravotti | Lp-spaces, Hölder and Minkovski inequality, Completions |
| January 10 | Lecture:Ravotti | |
| January 13 | Exercises: Ravotti | |
| Week 13 | Type | Topic/Material |
| January 16 | Lecture: Bruin | Convolutions, bounded functional, Chapter 15 |
| January 17 | Lecture: Bruin | |
| January 20 | Exercises: 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 | Type | Topic/Material |
| January 23 | Lecture:Bruin | Riesz Representation Lemma, Chapter 17 |
| January 24 | Lecture:Bruin | |
| January 26 | Exercises: Ravotti |
By oral examination on appointment.