Measure theory is the study of such fundamental ideas as length, area, volume, arc length and surface area. It is the basis for the integration theory used in advanced mathematics since it was developed by Henri Lebesgue in about 1900. Moreover, it is the basis for modern probability theory. The course starts by setting up measure theory and integration, establishing important results such as Fubini's Theorem and the Dominated Convergence Theorem which allow us to manipulate integrals. This is then applied to Fourier Analysis, and results such as the Inversion Formula and Plancherel's Theorem are derived. The Radon-Nikodyn Theorem provides a representation of measures in terms of a density. Probability theory is then discussed with topics including distributions and conditional expectation.
Unit details and rules
Academic unit | Mathematics and Statistics Academic Operations |
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Credit points | 6 |
Prerequisites
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A mark of 65 or greater in 12 credit points of MATH2XXX units of study |
Corequisites
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None |
Prohibitions
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MATH4069 |
Assumed knowledge
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Real analysis and vector spaces. For example MATH2X21 and MATH2X23 |
Available to study abroad and exchange students | Yes |
Teaching staff
Coordinator | Florica-Corina Cirstea, florica.cirstea@sydney.edu.au |
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Lecturer(s) | Florica-Corina Cirstea, florica.cirstea@sydney.edu.au |