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.

**Aantal college-uren**

2

**Tentaminering**

Mondeling of schriftelijk tentamen + huiswerk

**Verplichte literatuur**

H. Bauer, Measure and integration theory, de Gruyter (2001). *Werkvorm *

Hoorcollege en werkcollege *Homepage *

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