Elementary approaches to classic strong laws of large numbers use a monotonicity argument or
a Tauberian argument of summability theory.
Together with results on variance of sums of dependent random variables they allow to
establish various strong laws of large numbers in case of dependence, especially under
mixing conditions.
Strong consistency of nonparametric regression estimates of local averaging type (kernel
and nearest neighbor estimates), pointwise as well as in L_2, can be considered as a
generalization of strong laws of large numbers.
Both approaches can be used to establish strong universal consistency in the case of
independence and, mostly by sharpened integrability assumptions, consistency under
rho-mixing or alpha-mixing.
In a similar way Rosenblatt-Parzen kernel density estimates are treated.