ON THE CONVERGENCE OF EMPIRICAL PROCESSES OF MIXING VARIABLES1

Conditions are given for the weak convergence of (t—t²)L_N(a_N^-1( t )) to a Gaussian process where v<1/2, a _N is a cdf and L _N is the normalized weighted empirical cumulative distribution function (cdf) for an α-mixing sample of random variables in R which may be non-stationary with discontinuous marginals.