Mathematics: Specialised Course in Integration Theory

<p>The course is an alternatively compulsory course within the Master's programme in mathematics. The course gives a presentation of some central results in integration theory, as well as the modern measure-theoretic approach to differentiation of functions. The students will be provided with a powerful and general machinery leading to a deeper understanding of aspects of modern analysis, like for example, harmonic analysis.</p><p>The course treats basic properties of signed and complex measures:</p> <ul> <li>Hahn and Jordan decomposition,</li> <li>absolute continuity and the Radon-Nikodym theorem, singularity, Lebesgue decomposition of measures,</li> <li>differentiability of finite Borel measures on Rd, differentiability of absolutely continuous functions,</li> <li>the Hardy-Littlewood maximal function and the weak type estimate for it,</li> <li>the Hardy-Littlewood maximal function of Lp-functions, p>1.</li> </ul><p>http://www.maths.lu.se/</p>