Solution (source code)

= Solution

The <strong law of large numbers> says that, for real <independent and identically distributed random variables> $Z_1,Z_2,\ldots$ with $\mathbb E|Z_1|<\infty$,
$$
\boxed{\mathbb P\!\left(\frac1n\sum_{i=1}^n Z_i\longrightarrow\mathbb E Z_1\right)=1.}
$$
The assertion is <almost sure convergence> of the entire sequence of <sample means>. Finite first absolute <moment> suffices; a finite <variance> is not required.