For official information, see also the course page on SISU.

 

Lecture: Thursdays and Fridays, 10:15-12:00 (MaD 381)

Start: Thursday, October 27, 2022

Exercises: Fridays, 8:30-10:00 (MaD 380), or Fridays, 12:15-14:00 (MaD 381)

Start: Friday, November 4, 2022

Course lecturer: Katrin Fässler

Course assistant: Ivan Violo

​

Credit points: 4

There are two alternative ways of passing the course:

​

1. Homework and course exam

(first exam date: December 14, 2022; second exam date: January 20, 2023).

There will be six exercise sheets with homework problems. To pass the course exam, it is necessary that at least 30% of all the homework problems have been solved and these solved problems then yield extra points in the course exam.

 

More information and the exercise sheets are posted here.

​

2. Final exam

(next exam date: March 10, 2023).

The course can also be passed by taking a final exam. Homework solutions are not required to participate in the final exam, but neither can they be used to gain extra points!

​

Language: Lectures are in English, exercises and exam can be solved in English or Finnish.

Here you can find a small English-Finnish measure and integration theory glossary.

​

Lecture material

[L] J. Lehrbäck: Mitta- ja integraaliteoria

​

Handwritten notes in English are posted here below. They follow closely the (Finnish) lecture notes by J. Lehrbäck and by T. Kilpeläinen.

​

Introduction

I. General measure theory - Yleistä mittateoriaa

1. Outer measure - Ulkomitta  [L, 12] (notes1, notes2)

2. Metric outer measures - Metriset ulkomitat [L, 13] (notes1, notes2)

3. Hausdorff measures - Hausdorffin mitat [L, 13] (notes1, notes2)

4. Abstract measure spaces - Abstraktit mitta-avaruudet [L, 11] (notes1, notes2)

II. General integration theory - Yleistä integraaliteoriaa

1. Integration theory (incl. absolute continuity) - Integraaliteoriaa [L, 14, 15] (notes1, notes2)

2. L^p spaces - L^p-avaruudet [L, 16] (notes1, notes2)

3. Fubini's theorem - Fubinin lause [L, 10.1, 17] (notes1, notes2)

Summary (notes)

​

Additional literature

• Tero Kilpeläinen: Mitta- ja integraaliteoria (chapters 10-14)

• Andrew M. Bruckner, Judith B. Bruckner & Brian S. Thomson: Real Analysis

• Avner Friedman: Foundations of Modern Analysis

• Terence Tao: An Introduction to Measure Theory (free preprint version available online)

• Elias M. Stein & Rami Shakarchi: Real Analysis

• Juha Kinnunen: Measure and Integral, lecture notes, Aalto University

​

​