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Measure, Integration and Probability - MATH5825
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Faculty: Faculty of Science
 
 
School:  School of Mathematics and Statistics
 
 
Course Outline: http://www.maths.unsw.edu.au/
 
 
Campus: Kensington Campus
 
 
Career: Postgraduate
 
 
Units of Credit: 6
 
 
EFTSL: 0.12500 (more info)
 
 
Indicative Contact Hours per Week: 3
 
 
Fee Band: 5 (more info)
 
 
Further Information: See Class Timetable
 
 

Description

Measure Theory provides one of the key building blocks of Analysis, Probability Theory, and Ergodic Theory and is an indispensable tool in the theory of differential equations, Harmonic Analysis, Mathematical Physics and Mathematical Finance.
In this course we will develop a proper understanding of measurable functions, measures and the abstract Lebesgue integral. A special attention will be paid to applications of Measure Theory in the Probability Theory such as construction of probability spaces for random variables and stochastic processes, Laws of Large Numbers, the Central Limit theorem and their applications. The Radon-Nikodym Theorem will be applied to introduce a general definition of conditional expectation.

Pre-requisites: 24 units of level III mathematics or a degree in a numerate discipline or permission of the Head of Department.

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