Last modified: 05 Aug 2021 13:04
Measure theory provides a systematic framework to the intuitive concepts of the length of a curve, the area of a surface or the volume of a solid body. It is foundational to modern analysis and other branches of mathematics and physics.
|Session||First Sub Session||Credit Points||15 credits (7.5 ECTS credits)|
Extension a measure from a semi-ring of sets to the corresponding ring of sets;
Algebras and σ-algebras of sets;
σ-additive and σ-semi-additive measures;
Lebesgue extension of a measure defined on a ring of sets;
Properties of the Lebesgue measure;
Definition and properties of measurable functions;
Convergence almost everywhere;
Measurable functions and uniform convergence; the Egorov theorem;
Lebesgue integral for simple functions;
The definition and the properties of the Lebesgue integral;
Absolute continuity and σ-additivity of the Lebesgue integral; the Chebyshev inequality;
The Lebesgue, the Levi and the Fatou convergence theorems for the Lebesgue integral;
Comparison of the Lebesgue integral and of the Riemann integral.
Information on contact teaching time is available from the course guide.
4 assignments (25% each)
Alternative Resit Arrangements for students taking course in Academic Year 2020/21
Resubmission of failed elements (pass marks carried forward).
There are no assessments for this course.
|Knowledge Level||Thinking Skill||Outcome|
|Factual||Remember||ILO’s for this course are available in the course guide.|