This course is discontinued

MAT9300 – Measure and integration

Course content

Measure theory includes sigma algebras, measure spaces, measurable functions, outer measures, construction measures, decompositions of measures, product measures. The theory of integration on measure spaces including the classical convergence theorems, various modes of convergence, product integration. Applications with emphasis on Lebesgue measure on R and the Lebesgue integral.

Learning outcome

Basic theory of measure and integration.

Admission

PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.

Prerequisites

Formal prerequisite knowledge

None.

Recommended previous knowledge

MAT2400 – Real Analysis/Error: java.lang.NullPointerException.

Overlapping courses

10 credits with Error: java.lang.NullPointerException.

10 credits with MA254/354.

10 credtis with Error: java.lang.NullPointerException.

*The information about the overlaps is not complete. Contact the department for more information if necessary.

Teaching

4 hours of lectures/exercises per week.

Examination

One compulsory assignment has to be handed in and approved. Final mark based on written examination at the end of the semester.


Rules for compulsory assignments at the Department of Mathematics (norwegian only).

Examination support material

No examination support material is allowed.

Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a pass/fail scale. Read more about the grading system.

Explanations and appeals

Resit an examination

This course offers both postponed and resit of examination. Read more:

Students who due to illness or other valid reason of absence were unable to sit for their final exams may apply for participation in deferred examinations. Deferred examinations are arranged either later in the same semester or early in the semester following the exam in question. Documentation of valid reasons for absence from the regular exam must be submitted upon application to participate in deferred examinations.

Students who have failed an exam, who withdraw during an exam, and students who wish to retake an exam to achieve a better grade may not participate in deferred exams, but may retake the exam when it is regularly scheduled.

Information about deferred and new examination (also called repeat examination) is found here

More information about examination at the Faculty of Mathematics and Natural Sciences can be found here

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Facts about this course

Credits

10

Level

PhD

Teaching

This version of the course is no longer held. Error: java.lang.NullPointerException will still be held.

Examination

Teaching language

English

The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian.