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

 

Lecture: Thursdays 10:15-12:00 and Fridays 10:15-12:00 in Agora Iota

(except Agora Epsilon, Friday, November 27)

Start: Thursday, October 29, 2026

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Exercises: Fridays 12:15-14:00 in Agora Iota

(except Tuesday, December 15, 2026, 14:15-16:00)

Start: Friday, November 6, 2026

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Course lecturer: Katrin Fässler

Course assistant: Guangzeng Yi

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Credit points: 4

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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.

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Lecture material

[L] J. Lehrbäck: Mitta- ja integraaliteoria (link)

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

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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)

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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

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