MATS112 Measure and Integration Theory 2 (4 cr)

Open the course unit brochure on Sisu
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028

Description

L^p -spaces, general measure spaces, measurable functions and integrals, s-dimensional Hausdorff measure.

Learning outcomes

After the course the student

  • understands the basics of L^p spaces (in particular L^2)
  • is able to define general outer measures and use the Caratheodory criterion for measurability
  • knows and uses the definitions of general measures and measurable functions in abstract measure spaces.
  • knows the basics of Hausdorff measures

Description of prerequisites

Introduction to mathematical analysis 3, Vector calculus 2, Vector analysis 1 and 2, Measure and integration 1

Study materials

Luentomoniste

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.

Completion methods

Method 1

Evaluation criteria:
Exam after the lectures. Extra benefits from approved homework assignments.
Time of teaching:
Period 2
Select all marked parts

Method 2

Evaluation criteria:
Final exam. At least 50% of total points is required for a passing grade.
Select all marked parts
Parts of the completion methods
x

Teaching (4 cr)

Type:
Participation in teaching
Grading scale:
0-5
Language:
Finnish

Teaching

x

Exam (4 cr)

Type:
Exam
Grading scale:
0-5
Language:
Finnish

Teaching