| Dato | Undervises av | Sted | Tema | Kommentarer / ressurser |
| 18.08.2009 | Erik Bédos (EB)? | Auditorium 2, VB ? | Introduction. Prologue. Sets and functions.? | Cf. Chapter 1 and 2 (first part). ? |
| 19.08.2009 | EB? | Aud. 4, VB? | Counting. Sigma-algebras.? | Cf. Chapter 2 (second part) and Chapter 3 (just the very beginning!). We will only sketch the proof of the CB-theorem (2.7). ? |
| 25.08.2009 | EB? | Aud. 2, VB? | Exercises. Sigma-algebras.? | We look at some of the following exercises from Ch.2 : 1 iv) v), 4 i), 5 i) iii) iv), 15, 21. Then we continue with Ch. 3. ? |
| 26.08.2009 | EB? | Aud. 4, VB? | Borel algebras. Measures.? | We finish Ch. 3 and continue with Ch. 4.? |
| 01.09.2009 | EB? | Aud 2, VB? | Exercises. Measures. ? | We look at the following exercises from the book : 3.4, 3.8, 4.4, 4.7, and at Extra-exercise 1 (mentionned during the lecture 26.08). Then we continue in Ch. 4.? |
| 02.09.2009 | EB? | Aud 4, VB? | Properties of measures. Dynkin systems.? | We first finish ch. 4. Then we continue with ch. 5. [Note : we didn't actually go through all of Thm 4.4, only the first part assuming that mu is a measure and deducing its continuity properties. Read the rest yourself !]. ? |
| 08.09.2009 | EB? | Aud 2 VB? | Exercises. Uniqueness of measures. ? | We first look at Extra-Exercise 2 and exercises 4.8, 4.10, 4.11 ( not ii)b) ), 4.12 and 5.2. Then we continue with ch. 5. [Exercise 4.13 is also recommended, but we won't have time to go through it; the solution will be given on the homepage, as for all exercises !].? |
| 09.09.2009 | EB ? | Aud 4 VB? | Uniqueness and existence of measures.? | We finish Ch. 5 and start to look at Ch. 6. ? |
| 15.09.2009 | EB? | Aud 2 VB? | Existence of measures: Caratheodory's theorem.? | We continue in ch. 6.? |
| 16.09.2009 | EB? | Aud 4 VB? | Exercises. Measurable mappings.? | We first look at the following exercises from the book : Ch. 5: 6, 8, 9; Ch. 6: 3, 4i), ii). Then we look at Ch. 7. ? |
| 22.09.2009 | EB? | Aud 2 VB? | Exercises. Measurable mappings.? | We look at the following exercises from Ch. 6 : 6, 8, 9, 10. Then we continue in Ch. 7. ? |
| 23.09.2009 | EB? | Aud 4 VB? | Measurable mappings and measurable functions.? | We finish Ch. 7 and begin in Ch. 8.? |
| 29.09.2009 | EB? | Aud 2 VB? | Exercises. Measurable functions.? | We look at the following exercises : 7.3, 7.9 i)-vi), 8.3 i), 8.4. Then we continue in Ch 8.? |
| 30.09.2009 | EB? | Aud 4 VB? | Measurable functions. Integration of simple functions.? | We finish Ch. 8. Then we begin in Ch 9. ? |
| 06.10.2009 | EB? | Aud 2 VB? | Exercises. Integration of positive functions? | We look at the following exercises from Ch. 8 : 7, 12, 15, 17. Then we continue in Ch. 9.? |
| 07.10.2009 | EB? | Aud 4 VB? | More integration.? | We finish Ch. 9 and begin in Ch. 10. ? |
| 13.10.2009 | EB? | Aud 2 VB? | Exercises. More integration.? | We look at exercises 5, 8 10 in Ch. 9. Then we continue in Ch. 10.? |
| 14.10.2009 | EB ? | Aud 4 VB? | Null sets. Convergence theorems.? | We finish Ch. 10 and look at the Monotone Convergence Theorem in Ch. 11.? |
| 20.10.2009 | EB? | Aud 2 VB? | Exercises. Lebesgue's dominated convergence theorem.? | We look at the following Extra-exercises and prove Lebesgue's convergence theorem in Ch. 11.? |
| 21.10.2009 | EB? | Aud 4 VB? | Parameter dependent integrals. Riemann vs Lebesgue integration.? | We continue in Ch. 11. ? |
| 27.10.2009 | EB? | Aud 2 VB? | Exercises. Improper Riemann integrals. Examples.? | We first look at Exercises 4 and 7 in Ch. 11. Then we finish Ch. 11.? |
| 28.10.2009 | EB? | Aud 4 VB? | L^p-spaces. ? | We look at Ch 12. [Note : Some proofs and some subsections will be omitted]. ? |
| 03.11.2009 | EB? | Aud 2 VB? | Exercises. L^p-spaces II. ? | We first look at exercises 11.9, 12.1 and 12.10. Then we continue with a few more results from Ch. 12. ? |
| 04.11.2009 | EB? | Aud 4 VB? | Product measures. ? | We look at Ch. 13 [Note : Some proofs and some subsections will be omitted]. ? |
| 10.11.2009 | EB? | Aud 2 VB? | Tonelli's theorem and Fubini's theorem. The Radon-Nikodym theorem.? | We continue in Ch. 13 (subsections 8, 9 and 11). Finally, we look at the following subsections in Ch. 19 : 1, 2 (not the proof !), 6-9. [This will be the last ordinary lecture.]? |
| 11.11.2009 | EB? | Aud 4 VB? | Exercises. ? | We look at the following exercises : from Ch. 13 : 4, 5, 7, 8; from Ch. 19 : 4, 5, 6. ? |
| 17.11.2009 | EB? | Aud 2 VB? | Exercises? | We look at some exercises picked from recent exams : Set 1 (in english).? |
| 18.11.2009 | EB? | Aud 4 VB? | Exercises.? | We look at some exercises picked from recent exams : Set 2 (in english) .? |
| 24.11.2009 | EB? | Aud 2 VB? | Exercises. ? | We look at some exercises picked from recent exams : we finish Set 2 and look at Set 3 (in english) . ? |
| 25.11.2009 | EB? | Aud 4 VB? | Open hours. ? | We will first comment the solution of some parts of the mandatory assignment. The rest of the time will be devoted to eventual questions from the audience.? |
Undervisningsplan
Published Aug. 13, 2009 12:05 PM
- Last modified Nov. 20, 2009 1:13 AM