A functional central limit theorem for [varrho]-mixing sequences

In this note a functional central limit theorem for [varrho]-mixing sequences of I. A. Ibragimov (Theory Probab. Appl. 20 (1975), 135-141) is generalized to nonstationary sequences (Xn)n [set membership, variant] , satisfying some assumptions on the variances and the moment condition E Xn2 + b = O(nb/2-[epsilon]) for some b > 0, [epsilon] > 0.