Probability and Measure, Lecture 5: Measurable Functions

This channel is now deprecated. Please find this video on my new channel: https://www.youtube.com/watch?v=eyWLekPzzuE&list=PL0vEWJI_pj7RZ51zecINlzWxpFv83r8RE&index=5 In preparation for defining the integral, we introduce the notion of both simple functions and measurable functions. We then state a bunch of useful properties regarding measurable functions. Note that simple or measurable random variables are just simple or measurable functions on a probability space.