Probability and Measure, Lecture 10: Convergence of Measures

This video begins with a discussion of weak convergence of measures and the Portmanteau Theorem. We then discuss convergence for random variables including convergence in distribution, in probability, almost surely, and in Lp or in pth moment. Lastly, we state and prove the Borel-Cantelli lemmas, which will be very useful for proving the strong law of large numbers in lecture video 11.

[cnca]

Hello Prof! Thanks you for the videos! I enjoy them a lot and your explanations clarified a lot of my confusions. Could you share a more up to date lecture note that includes SLLN and CLT? Thanks!