PMAT 42833: Measure Theory

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Course Code    : PMAT 42833

Title                   : Measure Theory

Pre-requisites   : PMAT 42793

 Learning Outcomes:

At the end of the course the student should be able to demonstrate knowledge of the concepts and theorems of abstract Measure Theory and to apply them in Lebesgue integrals.

 Course Contents:

Measure Theory: Algebra, -algebra, additivity properties of a set function, Measure, Borel sets, Lebesgue measure, outer Measure, measurable subsets, measurable functions, Integral, Properties that hold almost everywhere, integrable functions, Additivity Theorem, Monotone convergence theorem, Dominated convergence theorem, Fatou's lemma, Relation of Riemann and  Lebesgue integrals, Modes of convergence.

 Method of Teaching and Learning: A combination of lectures, tutorial discussions and presentations.

Assessment: Based on tutorials, tests, presentations and end of course examination.

 Recommended Reading:

  1. Cohn, D.L., (2nd edition, 2015) Measure Theory, Springer New York.
  2. Barra, G., (2nd edition, 2003) Measure Theory and Integration, Elsevier.

 

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