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