MAT4300 - Autumn 2009

Undervisningsplan

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.

Published Aug. 13, 2009 12:05 PM - Last modified Nov. 20, 2009 1:13 AM