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Measure theory (BM)



In this course we introduce an abstract concept of measure and integration on a so-called measurable space. For functions of a real variable, this leads to the Lebesgue integral which gives a broader class of integrable functions (than the classical Riemann integral). Measure theory is of crucial importance in probability theory, stochastic processes, ergodic theory,
and analysis.

Main subjects of this course are: premeasure, extension theorem of Caratheodory, measurable functions, integration of measurable functions, convergence theorems (Fatou, Lebesgue dominated convergence), L^p spaces, Holder and Minkowsky’s inequality, absolute continuity, Radon Nikodym theorem.

Students with interest in stochastics and/or analysis are also encouraged
to follow the Linear Analysis course.

Lecture hours

2 per week


Take-home assignments; final grade is calculated as the average over the marks for all assignments. A schedule with dealines for the assignements will be provided at the start of the course.

Obliged literature

H. Bauer, Measure and integration theory, de Gruyter (2001), ISBN 3-11-016719-0