A note on convergence to mixtures of normal distributions

Double arrays of random variables obtained by normalizing a sequence that is asymptotically close to a martingale difference sequence are considered, and conditions ensuring that the row sums converge in distribution to a mixture of normal distributions are found. The main condition is that the sums of squares in each row converge in probability to a random variable.Research sponsored in part by the Office of Naval Research, Contract # N00014-75-C-0809