Convergence of random variables 09 - Strong law of large numbers and ergodic theorem.

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This video gives a complete proof of the strong law of large numbers for random variables with finite variance using Chebyshev's inequality and the first Borel-Cantelli lemma. We also state (without proof) the ergodic theorem which extends the strong law of large numbers to stationary sequences of random variables that are not necessarily independent. This is Section 3.2 of my Stochastic Modeling book.
This video is part of the playlist Advanced Probability https://www.youtube.com/watch?v=qGsHiHwgInU&list=PLV3oHJg9b1NRhjCs7ZgkAj6US-8m2ymTB.