  Let $f(n)$ be a strongly additive complex valued arithmetic function. Under
mild conditions on $f$, we prove the following weighted strong law of large
numbers: if $ X,X_1,X_2,... $ is any sequence of integrable i.i.d. random
variables, then $$ \lim_{N\to \infty} {\sum_{n=1}^N f(n) X_n \over\sum_{n=1}^N
f(n)} \buildrel{a.s.}\over{=} \E X . $$
