Mathematics: Specialised Course in Integration Theory

This course explores advanced concepts in integration theory and equips you with general methods used in modern mathematical analysis. You’ll learn how to work with signed and complex measures, understand key theorems, and apply them in areas like harmonic analysis and probability theory. The course provides a solid foundation for further studies in analysis and related fields.

Topics covered include

• Hahn and Jordan decomposition
• Absolute continuity and the Radon–Nikodym theorem
• Singularity and Lebesgue decomposition of measures
• Differentiability of finite Borel measures on ℝᵈ
• Differentiability of absolutely continuous functions
• Riesz representation theorem
• Haar measures

The course is alternative-compulsory within the Master’s programme in Mathematics at Lund University and is also offered as a standalone course.

Teaching is delivered through lectures and seminars, where you will engage with both theory and practical problem-solving. You will work independently and in groups, and apply your knowledge in a specialised project.

Assessment is includes a take-home exam, a written report, and an oral presentation. Together, these components evaluate your ability to apply theoretical knowledge, communicate mathematical ideas clearly, and work independently.

After completing the course, you will be well-prepared for advanced studies in mathematics, especially in analysis, probability theory, and functional analysis. The skills you gain are valuable for academic research and can also be applied in industries where deep mathematical understanding is needed.

This course strengthens your ability to solve complex problems, communicate mathematical ideas clearly, and carry out independent work—skills that are essential whether you continue in academia or move into a professional role.

Entry requirements

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.

Selection criteria

Seats are allocated according to: ECTS (HPAV): 100 %.

Tuition fees for non-EU/EEA citizens

Citizens of countries outside:

• The European Union (EU)
• The European Economic Area (EEA) and
• Switzerland

are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.

Tuition fees, payments and exemptions

Full programme/course tuition fee: SEK 23,125
First payment: SEK 23,125

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Note that you may also need to pay an application fee, or provide proof of exemption.

Application fee

No tuition fees for citizens of the EU, EEA and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.