MM517: Measure and Integration Theory (5 ECTS)

STADS: 13001701

Level
Bachelor course

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

Teacher responsible
No responsible teachers found, contact the department if necessary

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

Comment:
Ansvarlig lærer: Magdalena Musat, lektor

Ubegrænset deltagerantal

Prerequisites:
None

Academic preconditions:
The content of MM501 Calculus I and MM502 Calculus II, MM505 Linear Algebra, MM508 Topologi I and MM509 Topologi 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
By the end of the course the student will be able to:

use the basic concepts of the theory, in particular sigma-algebras, measurability and integration
use the methods from the theory to solve concrete problems in Analysis, in particular concerning applications of the convergence theorems for integrals and Fubini's Theorem
give an oral presentation of the statements and proofs related to any subject on a previous given list of topics within the course syllabus
formulate the oral presentation a mathematically correct way
answer supplementary questions from the teacher and the external examiner on definitions and results from the course syllabus.

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 30 minutes oral exam with 30 minutes preparation and an external examiner. Marks according to the Danish 7-point marking scale.

Reexamination after 2. quarter.

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

(a) Forelæsninger (28 timer).
(b) Eksaminatorier/opgaveregning (21 timer).
Educational activities

Language
This course is taught in English, if international students participate. Otherwise the course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.