Measure Theory

Measure theory seeks to assign a measure, or quantity, to certain sets (typically in n-dimensional space) which is consistent, reasonably general, and agrees with our intuition of length, area and volume in familiar situations. With this, one can develop the Lebesgue theory of integration which has several advantages over the older Riemann integral. The material is fundamental to modern mathematical analysis, particularly stochastic processes and the mathematical models of financial markets.

Course Information

Most modules require a 2.2 degree in a related discipline or equivalent professional experience. Should you have any queries regarding your eligibility, please contact us at

N.B. Required honours undergraduate degree (Level 8) a 2:1 (or equivalent grade) BSc in Financial Mathematics, Mathematics, Applied and Computational Mathematics, or Statistics.

On successful completion of this module, the student is expected to be able to:

  • Appreciate the shortcomings in the Riemann integral and the necessity for the introduction of the Lebesgue integral;
  • Be familiar with the basic theory of sigma algebras, measurable functions and integrable functions;
  • Know the conditions under which it is possible to swap limits and integration;
  • Be familiar with applications of measure theory to functional analysis, potential theory and other areas of mathematics.

Learn from world renowned academic staff in Ireland’s leading, future focused and globally recognised colleges.

Gain an accredited NFQ qualification/micro credential that you may count towards a full award if you so wish in the future.

Previous modules may be used as recognition of prior learning towards Advance Centre degree programmes.

Equip yourself with the latest in demand skillset, tools, know-how and knowledge to succeed in your career.

Gain a competitive edge, influence growth and steer strategic goals in your organisation upon completion of your studies with the Advance Centre.

Yes, if you complete this module it can be credited as part of the MSc Financial Mathematics Full Time or MSc Financial Mathematics Part Time.

Detailed Course Information

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