Note: This is an archived Handbook entry from 2011.
|Dates & Locations:|| |
This subject has the following teaching availabilities in 2011:Semester 1, Parkville - Taught on campus.
Timetable can be viewed here. For information about these dates, click here.
|Time Commitment:||Contact Hours: 36 hours comprising one two-hour lecture per week and one one-hour practical class per week. |
Total Time Commitment: 120 hours
|Recommended Background Knowledge:||
Subjects in linear algebra (equivalent to 620-231 Group Theory and Linear Algebra) and metric spaces (equivalent to 620-329 Metric and Hilbert Spaces).
|Non Allowed Subjects:||None|
|Core Participation Requirements:||
For the purposes of considering requests for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements for this entry.
The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website: http://www.services.unimelb.edu.au/disability/
CoordinatorProf Arun Ram
Measure Theory formalises and generalises the notion of integration. 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 Lebesgue measure and integration, signed measures, the Hahn-Jordan decomposition, the Radon-Nikodym derivative, conditional expectation, Borel sets and standard Borel spaces, product measures, and the Riesz representation theorem.
After completing 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. They will also have an understanding of how these underpin the use of mathematical concepts such as volume, area, and integration and they will 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.
Up to 40 pages of written assignments (40%: two assignments worth 20% each, due mid and late in semester), a 3 hour written examination (60%, in the examination period).
|Prescribed Texts:|| |
|Recommended Texts:||W. Rudin. Real and Complex Analysis. McGraw – Hill. Third Edition. 1987. |
P. Halmos. Measure Theory. Springer. 1974.
|Breadth Options:|| |
This subject is not available as a breadth subject.
|Fees Information:||Subject EFTSL, Level, Discipline & Census Date|
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:
Master of Science (Mathematics and Statistics) |
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