|Lectures – Tue & Thu 14:15 - 16:00, Room M203.
Tutorials – will be fixed during the first class.
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.
Measurability; Lebesgue integral; Borel sets; Lebesgue measure; Lebesgue spaces; Absolute continuity; the Radon–Nikodym theorem; the Riesz representation theorem; Fubini's theorem
The course will be in English if necessary, in Finnish otherwise.
Walter Rudin: Real and Complex Analysis
see also Lecture notes by Bobby Hanson
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.
Analysis 1/Series and integration
Complex analysis 1 (useful but not necessary)