Measure Theory (MAST90012)
Graduate courseworkPoints: 12.5On Campus (Parkville)
Overview
| Availability | Semester 1 |
|---|---|
| Fees | Look up fees |
Measure Theory introduces the modern conceptual framework of analysis that has led to a transformation and generalisation of such basic objects as functions, and such notions as continuity, differentiability and integrability.
It is fundamental to many areas of mathematics and probability and has applications in other fields such as physics and economics. Students will be introduced to the core topics of Lebesgue's theory of integration, and abstract measure theory, in particular signed measures, the Hahn-Jordan decomposition, the Radon-Nikodym derivative. Additional topics may include rudiments of probability theory (conditional expectation, Borel sets and measures) and geometric analysis (rectifiable curves, Hausdorff measure and dimension).
Intended learning outcomes
On completion of this subject, students will:
- Understand the fundamentals of measure theory and be acquainted with the proofs of the fundamental theorems underlying the theory of integration;
- Understand how these underpin the use of mathematical concepts such as volume, area, and integration;
- Develop a perspective on the broader impact of measure theory in ergodic theory; and
- Have the ability to pursue further studies in this and related areas.
Generic skills
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- Problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- Analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- Collaborative skills: the ability to work in a team;
- Ttime-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 4 March 2025
Eligibility and requirements
Prerequisites
All of
| Code | Name | Teaching period | Credit Points |
|---|---|---|---|
| MAST20022 | Group Theory and Linear Algebra | Semester 2 (On Campus - Parkville) |
12.5 |
| MAST30026 | Metric and Hilbert Spaces | Semester 2 (On Campus - Parkville) |
12.5 |
Or equivalent
Corequisites
None
Non-allowed subjects
None
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 4 March 2025
Assessment
| Description | Timing | Percentage |
|---|---|---|
Continuing assessesment taking up to 40 hours, and worth 40% of the mark, throughout the semester.
| Throughout the semester | 40% |
A written examination
| During the examination period | 60% |
Last updated: 4 March 2025
Dates & times
- Semester 1
Coordinator Volker Schlue Mode of delivery On Campus (Parkville) Contact hours 36 hours comprising three 1-hour lectures per week Total time commitment 170 hours Teaching period 3 March 2025 to 1 June 2025 Last self-enrol date 14 March 2025 Census date 31 March 2025 Last date to withdraw without fail 9 May 2025 Assessment period ends 27 June 2025 Semester 1 contact information
What do these dates mean
Visit this webpage to find out about these key dates, including how they impact on:
- Your tuition fees, academic transcript and statements.
- And for Commonwealth Supported students, your:
- Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.
Last updated: 4 March 2025
Further information
- Texts
Prescribed texts
None
Recommended texts and other resources
Elias M. Stein & Rami Shakarchi, Real analysis : measure theory, integration, and Hilbert spaces Princeton lectures in Analysis, Vol III, Princeton University Press, 2005.
Terence Tao, An introduction to measure theory, Graduate Studies in Mathematics, AMS, 2011.
- Related Handbook entries
This subject contributes to the following:
Type Name Course Ph.D.- Engineering Course Doctor of Philosophy - Engineering Course Master of Philosophy - Engineering Course Master of Science (Mathematics and Statistics) Informal specialisation Mathematics and Statistics - Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
- Available to Study Abroad and/or Study Exchange Students
Last updated: 4 March 2025