# MA3105 Advanced real analysis, Spring 2010

### Announcements

* The final exam is oral and will be held on Friday, May 28th, from 14.00 to 15.00.Come by my office on Thursday or send an email to get the main topic for your presentation on the exam. The list of the topics is here .

* Next meeting is on April 16, 10.15-12.00, **room 922**

* March 10: We meet tomorrow, Thursday, March 11, at 10.15 in room 822, SBII

* March 3: We meet tomorrow, Thursday, March 4, at 14.15 in room 922, SBII

* February 20: There will be no meetings next week. The next lecture is on Tuesday, March 2nd. Problem set # 6 is your home midterm. Read section 12.1 from the book till Tuesday.

* January 19: There will be no lecture today and no problem session this week. The next lecture is on Friday, January 22, 10.15-12.00 in room 822, SB II. All Friday lectures are moved to 10.15-12.00.

* December 28: The first lecture is on Tuesday, January 12, 12.15 in room F6.

* December 28: If you are interested in taking the course and can not meet at the first lecture, please, send an e-mail to eugenia [at] math [dot] ntnu [dot] no

### Problems

14.01 Problem set 1 (PDF-file)

22.01 Problem set 2 (PDF-file)

29.01 Problem set 3 (PDF-file)

08.02 Problem set 4 (PDF-file)

15.02 Problem set 5 (PDF-file)

20.02 Problem set 6 (PDF-file)

05.03 Problem set 7 (PDF-file)

13.03 Problem set 8 (PDF-file)

15.04 Problem set 9 (PDF-file)

### Lectures

Tuesday 12:15-14:00, F6

Friday 12:15-14:00, F2

Thursday 15:15-16:00, F6 (problem session)

Lecturer: Eugenia Malinnikova

room 948, Sentralbygg II

phone 73550257

e-mail eugenia [at] math [dot] ntnu [dot] no

### Preliminary Curriculum

Signed measures and the Radon-Nykodym theorem.

Riesz-Markov theorem, the dual of C(X).

Mathematical model of probability, The Law of Large Numbers.

Dynamical systems and Ergodic Theorem.

Hausdorff measures and dimension

Fourier transform and applications.

We will mostly use the textbook:

McDonald, Weiss,* A course in Real Analysis*, Academic press.

More detailed plan of the lectures: Preliminary plan