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Lecture: Thursdays and Fridays, 10:15-12:00,

remote teaching: Zoom

Start: Thursday, October 29, 2020

Exercises: Thursdays, 14:15-16:00, or Fridays, 8:15-10:00

remote teaching: Zoom

Start: Thursday, November 4, 2020

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Registered participants have received the Zoom link via email, and it can also be found on Koppa. Please contact the lecturer if you would like to follow the course, but do not have access to the Zoom link.

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Credit points: 4

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Program

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Introduction (See these notes)

I. General measure theory - Yleistä mittateoriaa

1. Outer measure - Ulkomitta [K, 11], [L, 12]

2. Metric outer measures - Metriset ulkomitat [K, 12], [L, 13]

3. Hausdorff measures - Hausdorffin mitat [K, 12], [L, 13]

4. Abstract measure spaces - Abstraktit mitta-avaruudet [K, 13], [L, 11]

II. General integration theory - Yleistä integraaliteoriaa

1. Integration theory - Integraaliteoriaa [K, 14], [L, 14]

2. L^p spaces - L^p-avaruudet [K, 10], [L, 16]

3. Absolute continuity - Absoluuttinen jatkuvuus [L, 15, 17]​

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Study materials

[K] T. Kilpeläinen: Mitta- ja integraaliteoria (chapters 10-14)

[L] J. Lehrbäck: Mitta- ja integraaliteoria

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Additional literature

• Andrew M. Bruckner, Judith B. Bruckner & Brian S. Thomson: Real Analysis, 2008, www.classicalrealanalysis.com

• Avner Friedman: Foundations of Modern Analysis.

• Terence Tao: An Introduction to Measure Theory

• Elias M. Stein & Rami Shakarchi: Real Analysis.