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Measure theory and probability 734


 
Module code WTW 734
Qualification Postgraduate
Faculty Faculty of Natural and Agricultural Sciences
Module content

Measure and integration theory: The Caratheodory extension procedure for measures defined on a ring, measurable functions, integration with respect to a measure on a ?-ring, in particular the Lebesgue integral, convergence theorems and Fubini's theorem.
Probability theory: Measure theoretic modelling, random variables, expectation values and independence, the Borel-Cantelli lemmas, the law of large numbers. L¹-theory, L²-theory and the geometry of Hilbert space, Fourier series and the Fourier transform as an operator on L², applications of Fourier analysis to random walks, the central limit theorem.
Module credits 15.00
Prerequisites Real analysis on third-year level
Contact time 2 lectures per week
Language of tuition Module is presented in English
Department Mathematics and Applied Mathematics
Period of presentation Semester 1
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