probability - Proof explanation - weak law of large numbers

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Let $(X_i)$ be i.i.d. random variables with mean $\mu$ and finite variance. Then $$\dfrac{X_1 + \dots + X_n}{n} \to \mu \text{ weakly }$$ I have the proof here: What I don't understand is, why it

MathType on X: The Law of Large Numbers is a result in #probability that accounts for a very intuitive phenomena: The average of the results obtained from a large number of trials

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SOLVED: Let X1, X2 be independent and identically distributed random variables with E(Xi) = p, and let Sn = Î£(Xi - p). Assume that the moment generating function Mx(t) of X exists

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