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.
Study Type  Undergraduate  Level  4 

Session  First Sub Session  Credit Points  15 credits (7.5 ECTS credits) 
Campus  Aberdeen  Sustained Study  No 
Coordinators 

Syllabus
Extension a measure from a semiring of sets to the corresponding ring of sets;
Algebras and σalgebras of sets;
σadditive and σsemiadditive measures;
Measure spaces;
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 σadditivity 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. 
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