Discussion 13: Measurable Functions

In this discussion, we shall start questioning whether integrating functions on arbitrary sets is possible. We observe that to make sense of such a notion, we require an "additive structure" on the codomain and a measure structure on the domain. We then see another manner in which Riemann integrals (of continuous functions over compact intervals) can be defined. Keeping this newfound way of understanding Riemann integral, we define a class of functions between measure spaces, which we shall call measurable functions and then proceed to see a couple of properties of this class.