Stochastic Processes I - Lecture 04

[@johanneshappich5382]

am i getting this right that the WLOG in 1:20:40 ("a measurable functions is more or less an indicator function of a measurable set") is referring to the construction of Lebesgues-integral by approximation with simple functions, and hence the integration (i.e. expectation) properties of measurable functions are inherited from properties of simple functions and hence of characteristic functions?

[@MrBergengruen]

As long as you want to make very general statements about measurable functions typically you start with indicator functions and then pass to the general case by standard measure theoretic induction, for instance using the monotone class argument.