(eng): We investigate a nonparametric estimator of probability density introduced by A.R.Barron. Earlier papers established its consistency in a strong sense,e.g.,in the expected information divergence or expected chi-square divergence. This paper pays main attention to the expected chi-square divergence criterion. We give a new motivation of the Barron estimators by showing that a maximum-likelihood estimator (MLE) of a density from a family important in practice is consistent in expected information divergence.