MAT4410 – Advanced Linear Analysis
Schedule, syllabus and examination date
The course gives an introduction to more advanced topics in functional analysis and measure theory. Among the topics covered are: more Banach space theory (including the Banach-Steinhaus theorem, the open mapping theorem, the closed graph theorem and the Hahn-Banach theorem); more measure and integration theory (including product measures, Tonelli's and Fubini's theorems, signed measures, complex measures, Hahn's, Jordan's and Radon-Nikodym's theorems, conditional expectations, L^p /L^q-duality and Riesz' representation theorem, modes of convergence for measurable functions).
The course presents fundamental results of functional analysis and measure theory, and is the basis for further work in partial differential equations, stochastic analysis, and operator algebras. The students will learn to work with abstract measure spaces and with linear operators between infinite dimensional spaces.
Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.
Recommended previous knowledge
MAT1110 – Calculus and linear algebra, MAT1120 – Linear algebra, MAT2400 – Real Analysis and MAT3400 – Linear analysis with applications/MAT4400 – Linear analysis with applications. The course should be taken together with or after MAT3500 – Topology/MAT4500 – Topology.
- 5 credits overlap with MAT3300 – Measure and integration (discontinued)
- 5 credits overlap with MAT4300 – Measure and integration (discontinued)
- 2 credits overlap with MAT4340 – Elementary functional analysis (discontinued)
- 3 credits overlap with MAT4350 – Functional analysis (discontinued)
* For information about the potential partial overlap with other courses, contact the Department.
4 hours of lectures/exercises per week throughout the semester.
Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.
Final written examination.
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.
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.
Explanations and appeals
Resit an examination
Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.
Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.
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.
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.