Mathematics: Specialised Course in Integration Theory

Utbildningsfakta

Kod: MATP39

<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>

Behörighet

For admission to the course, English 6/B and at least 90 credits in mathematics are required, in which should be included the course MATM39 Integration theory, 7.5 credits, or equivalent.

Utbildningstillfällen

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• Mathematics: Specialised Course in Integration Theory

  Lund University

  Lund

  Startdatum: 18 januari 2027

  Slutdatum: 28 mars 2027

  Studietakt: 50 %