Abstract measure theory

Lectures – Tue & Thu 14:15 - 16:00, Room M203.
Tutorials – will be fixed during the first class.
Lecturer
Peter Hästö
Announcements
6.9 tutorials will be Mondays, 8:30-10, in M203, starting 12.9
8.9 set #1 = ch1: 1,3,5a,6
15.9 set #2 = ch1: 4,7,8,13
---- set #3 = ch1: 9,10,11,12
---- set #4 = ch2: 1,2,3,4
6.10 set #5 = ch2: 7,8,19, ch6: 1
14.10 set #6 = ch6: 2,5, ch8: 1,2
18.10 set #7 = ch8: 3,7,12
18.10 No class Thu 20.10 or Tue 25.10; final class Thu 27.10

In period 1 of the Fall term 2011 (Sept 6 – Oct 20) I will lecture a course on abstract measure theory, 802651S. This is an advanced course worth 5 credits.

This course is an abstract and demanding version of the course Lebesgue measure and integration (802653S; formerly Analysis III). It can be taken both by students who have completed this course, and by those who have not. Basic concepts from abstract topology will be very briefly reviewed, but ideally participants will have prior acquaintance with them.

The course is strongly recommended for students who intend to specialize in analysis at the master's or PhD level.

Contents
Measurability; Lebesgue integral; Borel sets; Lebesgue measure; Lebesgue spaces; Absolute continuity; the Radon–Nikodym theorem; the Riesz representation theorem; Fubini's theorem

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

Course textbook
Walter Rudin: Real and Complex Analysis
see also Lecture notes by Bobby Hanson

Evaluation
The course grade is based on completed exercises. There are about 4 exercices in each of 7 sets. 80% solved gives grade 5, 40% gives 1.

Prerequisites
Analysis 1/Series and integration
Topology (recommended)
Complex analysis 1 (useful but not necessary)