In this course we introduce an abstract concept of measure and integration on as 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 and 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.
Aantal college-uren
2
Tentaminering
Mondeling tentamen
Verplichte literatuur
H. Bauer, Measure and integration theory, de Gruyter (2001).
Werkvorm
Hoorcollege en werkcollege