Measure theory provides a foundation for many branches of mathematics such as harmonic analysis, ergodic theory, theory of partial differential equations and probability theory. It is a central, extremely useful part of modern analysis, and many further interesting generalizations of measure theory have been developed. It is also subtle, with surprising, sometimes counter-intuitive, results. The aim of this course is to learn the basic elements of Measure Theory, with related discussions on applications in probability theory. The Key contents covered will be:
The following main topics are contained in the course: Sigma-algebras and measures, measurable mappings, integration with respect to measures, the Lebesgue measure on the real line and on Rk, product measures, Lp-spaces.