MM817: Measure and Integration Theory (5 ECTS)

STADS: 13007001

Level
Master's level course

Teaching period
The course is offered in the autumn semester.
1st quarter

Teacher responsible
Email: szymanski@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal. Kurset kører i 1. kvartal. Fælles undervisning med MM517.

Prerequisites:
None

Academic preconditions:
The content of MM501 Calculus I and MM502 Calculus II, MM505 Linear Algebra, MM508 Topology I and MM509 Topology II must be known.

Course introduction
The aim of the course is to give a solid presentation of Measure and Integration Theory and thereby give an introduction to modern Functional Analysis. The course will also give the mathematical foundation for modern Probability Theory.

Expected learning outcome
At the end of the course the student will be able to:
- reproduce and illustrate definitions within the syllabus of the course in a precise mathematical language
- reproduce results, together with complete proofs, within the syllabus of the course in a precise mathematical languange
- relate the results within the syllabus of the course to each other
- apply the theory to solve problems within the scope of the syllabus of the course, including motivating the steps in the solutions
- use methods from measure theory to solve concrete problems in analysis and probability theory, such as convergence problems and problems involving product measures
- compare the Riemann integra integral to the Lebesgue integral and discuss the advantages of the latter

Subject overview
Sigma-algebras and measures, measurable mappings, integration with respect to measures, the Lebesgue measure on the real line and on Rk, product measures, Lp-spaces.

Literature

Meddeles ved kursets start.

Syllabus
See syllabus.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
a) Mandatory exercises, pass/fail, internal evaluation by teacher. The exercises must be passed in order to take the oral exam.
b) Oral examination, grades according to the dansih 7-point scale and external censorship.

Reexamination after 2nd quarter.

Expected working hours
The teaching method is based on three phase model.

Forelæsninger: 28 timer
Eksaminatorietimer/opgaveregning: 24 timer
Educational activities

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.