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Let s {; X n s};, n⩾ 1, be a stationary α-mixing sequence of real-valued rv's with distribution function (df) F, probability density function (pdf) f and mixing coefficient α (n). The df F is estimated by the empirical df F n, based on the segment X 1,…, X n. By means of a mixingale argument, it is shown that F n (x) converges almost surely to F (x) uniformly in x∈ R. An alternative approach, utilizing a Kiefer process approximation, establishes the law of the iterated logarithm for sups {; vb; F n (x)− F (xvb;; x∈ R. The df F is also estimated by a smooth estimate F n, which is shown to converge almost surely (as) to F, and the rate of convergence of sups {; vb; F n (x)− F (x) vb;;|; x∈ R s}; is of the order of O ((log log n/n) 1 2). The pdf f is estimated by the usual kernel estimate f n, which is shown to converge as to f uniformly in x∈ R, and the rate of this convergence is of the order of O ((log log n/nh 2 n) 1 2), where h n is the bandwidth …