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

 

Final exam: Thu 17.12.2026, 8.00–11.00, Agora, Ag B434.1 Lambda

Final exam, retake: Fri 22.1.2027. 13.00–16.00, Agora, Ag A102 Auditorio 1

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)

 

Exercises

sheet 1 (outer measure)

sheet 2 (metric outer measures)

sheet 3 (Hausdorff measures)

sheet 4 (abstract measure spaces)

sheet 5 (integration theory)

sheet 6 (L^p spaces)

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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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