MATM29 Specialised Course in Integration Theory is an optional course for a Master of Science degree in mathematics.
The material continues the development from the course 'MATM19 Integration Theory'' and covers the part sometimes called ''differentiation''. More precisely, it begins with Jordan and Hahn decompositions for signed measures, the Radon-Nykodim theorem and the Lebesgue decomposition, singular Lebesgue-Stieltjes measures and absolutely continuous functions and then the course turns the differentiation of functions and measures, the Hardy-Littlewood maximal function and the Hardy-Littlewood theorem about the maximal functions of $L^p$ functions.
The teaching consists of lectures and seminars. Compulsory hand-in exercises may be given.
The course is assessed through an oral examination, but the points can also be awarded based on presentations of parts of the above material.
Donald L. Cohn, Measure Theory, 2nd ed, 2013, ISBN: 978-1-4614-6955-1.
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