Past exam of the probability course of the University of Oxford / 2015 / 3 / a / Solution

The strong law of large numbers says that, for real independent and identically distributed random variables $Z_1,Z_2,\dots$ with $\mathbb{E}|Z_1|<\infty$,The assertion is almost sure convergence of the entire sequence of sample means. Finite first absolute moment suffices; a finite variance is not required.