Modern Real Analysis, 802631S

Lectures – Tuesdays and Fridays 2:15 – 4:00 pm, Room M203.
Tutorials – Thursdays 10 - 12 in SÄ112.
Peter Hästö
17.1 Lecture notes
23.1 Problem set 1: 12, 13, 14, 17, 19 (at the end of the lecture notes)
27.1 Problem set 2: 23, 27, 30, 43, 45 (at the end of the lecture notes)
3.2 Problem set 3: 46, 47, 52, 55, 57 (at the end of the lecture notes)
10.2 Problem set 4: 32, 33, 59, 60, 62 (at the end of the lecture notes)
17.2 Problem set 5
25.2 Problem set 6
2.3 Problem set 7
22.3 Problem set 8
22.3 Ei luentoa 27.3!
31.3 Problem set 9
13.4 Problem set 10
20.4 Problem set 11

In periods 3–4 of the Spring term 2012 (Jan 13–Apr 23) I will lecture a course on Modern Real Analysis, 802631S. This is an advanced course worth 10 credits.

The first part of the course (Jan 13–Mar 1) follows the structure of previous years and deals with Lebesgue spaces of integrable functions and their properties (Hölder and Minkowski inequalities, duality, completeness, approximation, etc. ).

The second part of the course (Mar 13–Apr 23) is new and deals with differentiable functions, in particular with the space of functions of bounded variation (BV-functions). Also some applications to variational problems will be presented. This part of the course can be taken by students who have previously completed the course Modern Real Analysis, for 5 additional credits.


The course will be in English if necessary, in Finnish otherwise.


Lecture notes
Ambrosio, Fusco & Pallara: Functions of Bounded Variation and Free Discontinuity Problems
Evans & Gariepy: Measure Theory and Fine Properties of Functions
Rudin: Real and Complex Analysis


The course grade is based on a final exam; additional points are given for completed exercises.


Lebesgue Measure and Integration 802653S
Abstract Measure Theory 802651S