Overview
Measure theory is one of the few theories which permeates all core mathematical domains (pure, applied and statistics). We develop Lebesgue integration and probability theory from the core elements of measure theory. The initial background will be kept to a minimum. In particular, it is only required knowledge of real … For more content click the Read More button below.
The unit will cover such pure topics as: semi-rings, algebras, and sigma-algebras of sets, measures, outer measures, the Lebesgue and Borel measures, construction of Vitali sets, construction of non-Borel Lebesgue measurable sets, measurable and integrable functions, the Lebesgue integral and the fundamental theorems, change of variables formula in Euclidean space, the Lebesgue spaces, iterated measures and the Fubini theorem, modes of convergence, signed measures, decomposition of measures and the Radon-Nikodym theorem, approximation results for the Lebesgue measure, Hausdorff measure and dimension, Haar measures, ergodic measures.
The unit will also cover topics which are essential for probability theory: such as Borel-Cantelli Lemma, independence, Kolmogorov 0-1 law, exponential bounds, conditional expectation, martingales.
Offerings
S1-01-CLAYTON-ON-CAMPUS
Rules
Enrolment Rule
Contacts
Chief Examiner(s)
Dr Andrea Collevecchio
Unit Coordinator(s)
Dr Andrea Collevecchio
Notes
This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. If you are enrolled in MTH5099 you will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4099. The assignments and exam in this unit will use some common items from the MTH4099 assessment tasks, in combination with several higher level questions and tasks.
Assessment
1 - Continuous assessment
2 - Examination (3 hours and 10 minutes)
Scheduled and non-scheduled teaching activities
Applied sessions
Lectures
Workload requirements
Workload
Other unit costs
Costs are indicative and subject to change.
Miscellaneous items required (Printing, Stationery)- $100.
Availability in areas of study
Master of Mathematics