New is a short version of the lecture notes on Measure theoretic probability, that contains all material treated in the lectures of this course (and a little more for the sake of completeness). The numbering in the first Programme below refers to the full version of the lecture notes, the alternative second part for the first three weeks refers to the numbering of the short set of lecture notes.
| 1 |
Class: From Spreij, Sections 1.1 (skip the cardinality part), 1.2, 1.3, (most of) 1.4, Most of 3.1 (ignore everything on topology), 3.2 (skip the proof of Theorem 3.10), 3.3 (up to Corollary 3.13) .
Tutorial: Make Exercises 1.6, 1.9, 3.2, 3.4. Homework: Make Exercises 1.1, 1.2, 1.4, 3.1; Read Section 1.5, Proposition 3.12 with the proof and the statement of Theorem 3.6. |
| 2 |
Class: Most of Sections 4.1 (some tedious proofs will be skipped), 4.2 (without Lemma 4.20), 4.4 (without Propositions 4.30, 4.31), 4.6 (up to Proposition 4.42), 5.1 up to Theorem 5.5 (ignore Remark 5.2), very brief mentioning of Section 5.2.
Tutorial: Make Exercises 4.3, 4.4, 4.9, 5.4. Homework: Make Exercises 4.10, 4.12, 5.5, 5.6. Have a glance at the main issues of Section 5.2. |
| 3 |
Class: Section 6.4: Proposition 6.8 only. Take all "measures" in this chapter as the usual positive measures! Section 6.5 (without proofs); Chapter 8: introduction, Most of Section 8.1 without Theorem 8.6 and Example 8.8 and not all proofs. General idea of Section 8.2.
Tutorial: Make Exercises 6.4, 6.7, 8.1, 8.6 . Homework: Make Exercises 6.6 (optional), 6.9, 8.3. |
| 4 |
Class: Chapter 1 of Van der Vaart, and most parts of Sections 2.1 and 2.2. Chapter 6 (Appendix) is supposed to be known.
Tutorial: Chapter 1: Exercises 1, 6, 7, 15, 21. Homework: Chapter 1: Exercises 12, 25; and optional: 19, 20a, 22. |
| 5 |
Class: Sections 2.3, 2.4, first part of Section 2.5; Sections 3.1, 3.3, perhaps Section 3.2.
Tutorial: Chapter 2: Exercises 9+10, 11; Chapter 3: 4, 20. Homework: Chapter 2: Exercises 3, 4; Chapter 3: 1, 11, 12. |
| 6 |
Class: Sections 4 and 4.1.
Tutorial: Chapter 4: Exercises 1, 2, 5. Homework: Chapter 4: Exercises 3, 6, 7. |
| 7 |
Class: Sections 4.2 (but not Subsection 4.2.1) and 4.3.
Tutorial: Chapter 4: Exercises 4, 12, 13, 21. Homework (optional!): Chapter 4: Exercises 10, 11(i,ii), 19, 23. |
| 1 |
Class: From Spreij, Sections 1.1, 1.2, 1.3, (most of) 1.4, Most of 2.1 (ignore everything on topology), 2.2 (skip the proof of Theorem 2.10), 2.3 (up to Corollary 3.13) .
Tutorial: Make Exercises 1.6, 1.9, 2.2, 2.4. Homework: Make Exercises 1.1, 1.2, 1.4, 2.1; Read Section 1.5, Proposition 2.12 with the proof and the statement of Theorem 2.6. |
| 2 |
Class: Most of Sections 3.1 (some tedious proofs will be skipped), 3.2, 3.4 (without Propositions 3.29, 3.30), 3.5 (up to Proposition 3.34), 4.1 up to Theorem 4.5, very brief mentioning of Section 4.2.
Tutorial: Make Exercises 3.3, 3.4, 3.9, 4.4. Homework: Make Exercises 3.10, 3.12, 4.5, 4.6. Have a glance at the main issues of Section 4.2. |
| 3 |
Class: Section 5.1: mainly Proposition 5.3 only, Section 5.2; Section 6.1, most of Section 6.2 without Theorem 6.7 (not all proofs). General idea of Section 6.3.
Tutorial: Make Exercises 5.1, 5.4, 6.1, 6.6. Homework: Make Exercises 5.3 (optional), 5.5, 6.3. |