Probability and Measure, Lecture 2: Carathéodory's Extension Theorem

This channel is now deprecated. Please find this video on my new channel:    • Probability and Measure, Lecture 2: Carath...   In this video lecture, we prove Carathéodory's Extension Theorem. This theorem allows us to take a pre-measure defined on a ring or semi-ring and extend it to a measure on a sigma field. It will be a useful tool for constructing measures such as Lebesgue measure. My written lecture notes can be found at https://sites.ualberta.ca/~kashlak/ka...