17.09.2012 - 07.10.2012

- 17.09.2012 (Monday) 16:15-17:45 in V2-200
- 18.09.2012 (Tuesday) 16:15-17:45 in V2-200
- 20.09.2012 (Thursday) 15:30-17:50 in V2-200
- 24.09.2012 (Monday) 15:30-17:50 in U5-133
- 25.09.2012 (Tuesday) 15:30-17:50 in U5-133
- 27.09.2012 (Thursday) 16:15-17:45 in U5-133
- 01.10.2012 (Monday) 16:15-17:45 in V2-200
- 02.10.2012 (Tuesday) 16:15-17:45 in V2-200
- 04.10.2012 (Thursday) 15:30-17:50 in U5-133

- Mondays 16:15-17:45 in T2-204
- Tuesdays 16:15-17:45 in T2-204
- 02.11.2012 (Friday) 12:15-13:45 in T2-241 (Lecture instead of tutorial)
- 09.11.2012 (Friday) 12:00-13:50 in V2-216 (Midterm Exam instead of tutorial)
- 07.12.2012 (Friday) 12:15-13:45 in V2-216 (Lecture instead of tutorial)

Jacod, J. and Protter, P., Probability Essentials, 2nd edition (corrected 2nd printing), Springer, 2004. [Chapters 1-21]

Rudin, W., Real and Complex Analysis, 3rd edition, McGraw-Hill, 1987. [Chapters 1, 3 and 8]

Dudley, R. M., Real Analysis and Probability, Cambridge University Press, 2002. [Chapters 3, 4, 8 and 9]

- Midterm Exam: 09.11.2012 (Friday) 12:00-13:50 (Sharp) in V2-216

A copy of this version of the lecture note was distributed at the midterm exam.

Exam coverage- Lecture note: Chapters 0, 1 and 2 (Sections 2.5 and 2.7 excluded)
- Problem sets: all Problems and all Exercises up to Problem set 8

- Final Exam: 18.12.2012 (Tuesday) 16:00-17:50 (Sharp) in T2-204

A copy of this version (updated on 07.12.2012) of the lecture note was distributed at the final exam.

Exam coverage- Lecture note: Section 2.7 and Chapters 3 and 4, with the following contents excluded:

Lemma 3.62, Section 3.6, Theorem 4.36, Lemma 4.37, Definition 4.40, Theorem 4.41, Proposition 4.42 and Theorem 4.43. - Problem sets: all Problems and all Exercises from Problem set 9 to Problem set 14
- (The exam coverage of Midterm Exam is treated as prerequisites.)

- Lecture note: Section 2.7 and Chapters 3 and 4, with the following contents excluded:

- Fridays 12:15-13:45 in V2-216 (There is no tutorial on 21.12.2012.)
- 05.11.2012 (Monday) 16:15-17:45 in T2-204 (Tutorial instead of lecture)
- 06.11.2012 (Tuesday) 16:15-17:45 in T2-204 (Tutorial instead of lecture)
- 10.12.2012 (Monday) 16:15-17:45 in T2-204 (Tutorial instead of lecture)
- 11.12.2012 (Tuesday) 16:15-17:45 in T2-204 (Tutorial instead of lecture)

- Lecture note pdf file (618KB) (version of 07.12.2012)

The deadlines are specified at the beginning of each problem set. There are two types of problems:

unless otherwise stated, whereas

submitting his/her solutions to the problem sets

Also it is

to submit his/her solutions written in his/her own words.

- Problem set 1 (Submission of solutions not required; meant only for discussion in the tutorials.)
- Problem set 2
- Problem set 3 (Some wrong dates have been fixed.)
- Problem set 4 (Some wrong dates have been fixed.)
- Problem set 5
- Problem set 6
- Problem set 7 (The deadline is 12:00 (sharp) on 02.11.2012 (Friday) since the corresponding tutorial is on 05.11.2012 (Monday).)
- Problem set 8 (Submission of solutions not required; meant only for discussion in the tutorial.)
- Problem set 9
- Problem set 10
DO NOT SKIP
**Exercise 3.11**when writing your solutions.**Exercise 3.11**is not difficult and

will be treated in detail in the tutorial although it is classified as**Exercise**in regards to the assigned points. - Problem set 11
- Problem set 12
This time most problems are just simple applications of
**Theorem 3.61**and**Theorem 4.4**.

Please try to understand these two theorems. - Problem set 13
(The deadline is 16:15 (sharp) on
**11**.12.2012 (Tuesday) since the corresponding tutorial is on this same day.)

REMARK: Please DO NOT SKIP the Exercises when writing solutions to Problem set 13.

The Exercises in this problem set are not difficult and will be treated in detail in the tutorial although they are classified as Exercises. - Problem set 14 (Submission of solutions not required; meant only for discussion in the tutorial.)

Naotaka Kajino

Department of Mathematics,
Graduate School of Science,
Kobe University,

Rokkodai-cho 1-1, Nada-ku, 657-8501 Kobe, Japan

Office: Faculty of Science Building B, Room B426

Tel: +81-78-803-5616

Fax: +81-78-803-5610

E-mail: nkajino ``at" math.kobe-u.ac.jp