Let X1 , X2 , X3, … Xn be iid random variables. Laws of large numbers roughly state that the average of these variables converges to the expectation value of each of them when n is large. Various forms of these laws have many applications. The strong and weak laws along with the following three applications will be discussed: a) Coin-tossing. b) The Weierstrass approximation theorem. c) The Glivenko–Cantelli theorem.
In the second half of this talk, a law of large numbers is proven for spaces with infinite “volume” (measure) as opposed to the above version for probability measures (“volume” =1).