MATS113 Advanced Measure Theory (5 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023
Description
Basics about Borel and Souslin sets, measurable choices and partitions, conditional measures, disintegration of measures and ergodic theorems. Other possible topics include Egoroff and Lusin theorems, extensions of measures, weak convergence and Prokhorov theorem.
Depending on the audience the course will be lectured either in Finnish or in English.
Learning outcomes
After the course students are expected to understand the basics of Borel and Souslin sets and conditional measures and to be able to prove and apply measurable selection and disintegration theorems.
Description of prerequisites
Measure and integration theory 1 and 2
The courses Real analysis and Functional analysis will be useful.
Study materials
lecture notes
Literature
- V.I. Bogachev, Measure Theory
Completion methods
Method 1
Evaluation criteria:
course exam points and exercise points
Select all marked parts
Method 2
Evaluation criteria:
final exam points
Select all marked parts
Parts of the completion methods
x
Participation in teaching (5 cr)
Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
course exam points and exercise points
Language:
Finnish
Study methods:
lectures and exercises
x
Exam (5 cr)
Type:
Exam
Grading scale:
0-5
Evaluation criteria:
final exam points
Language:
English, Finnish