On the rate of complete convergence for weighted sums of arrays of random elements

Let {V-nk, k >= 1, n >= 1} be an array of rowwise independent random elements which are stochastically dominated by a random variable X with E|X| (gamma)/(alpha+0) log(rho)(|X|) < infinity for some rho > 0,alpha > 0,gamma > 0, > 0 such that theta+alpha/gamma < 2. Let {ank, k >= 1,n >= 1} be an array of suitable constants. A complete convergence result is obtained for the weighted sums of the form Sigma(infinity)(k=1) a(nk)V(nk).