I'm reading Feller's An introduction to Probability theory and Its Application. I don't know how to prove when lln doesn't hold. I just know that the sufficient condition for the lln to hold is that $\sqrt{Var(S_n)}/n \rightarrow 0$.
For example: Let {$X_k$} be mutually independent and have a common distribution
with mean $\mu$ and finite variance. If $S_n = X_1 + \cdots + X_k$, prove that lln does not hold for the sequence {$S_n$} but holds for $a_nS_n$ if $na_n \rightarrow 0$.
What should i do know?
2026-03-31 14:28:31.1774967311
How to prove law of large numbers doesn't hold
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