Can you prove the Law of Large Numbers?

Question

So clearly it is not hard to experimentally prove that the more times something is done, say rolling a die, the closer your experimental results come to your theoretical likelihoods, but is there a mathematical way to show why this occurs?

Thanks

Answer 1

Yes, most proofs prove the Chebychev inequality and then use that to prove the law of large numbers. http://en.wikipedia.org/wiki/Law_of_large_numbers#Proof_using_Chebyshev.27s_inequality