Starkes Gesetz der großen Zahlen

Let $X_i$ be a sequence of independent identically distributed Random Variables with finite Expectation then we have: $\mathbb{P}\left({\lim }_{n\to \infty }{\bar{X}}_{(n)}=\mu \right)=1$ for $n\to \infty$ p-fast sichere Konvergenz

in other words, if we have a sequence of random variables, their Arithmetic Mean will converge to the Expectation with a probability of $1$ as $n$ goes to infinity.