MATH30360 Measure Theory and Integration

Academic Year 2023/2024

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

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Curricular information is subject to change

Learning Outcomes:

On successful completion of this module the student should 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.

Student Effort Hours: 
Student Effort Type Hours
Specified Learning Activities


Autonomous Student Learning








Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning. 
Requirements, Exclusions and Recommendations

Not applicable to this module.

Module Requisites and Incompatibles
MATH10320 - Mathematical Analysis

MATH40430 - Measure Theory & Integration, MATH40790 - Measure Theory (online)

Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Continuous Assessment: Continuous assessment Varies over the Trimester n/a Standard conversion grade scale 40% No


Examination: Exam 2 hour End of Trimester Exam No Standard conversion grade scale 40% No



Carry forward of passed components
Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Feedback individually to students, post-assessment

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