On the Glivenko-Cantelli theorem for generalized empirical processes based on strong mixing sequences

Given \s{Xi, i [greater-or-equal, slanted] 1\s} as non-stationary strong mixing (n.s.s.m.) sequence of random variables (r.v.'s) let, for 1 [less-than-or-equals, slant] i [less-than-or-equals, slant] n and some [gamma] [epsilon] [0, 1], F1(x)=[gamma]P(Xi 0, and a rate for the almost sure convergence of Dn are obtained under strong mixing. These results generalize those of Singh (1975) for the independent and non-identically distributed sequence of r.v.'s to the case of strong mixing.Generalized empirical processes strong mixing almost sure convergence