Right closure of martingale sequences in the sense of theA-integral

In this paper new sufficient (necessary and sufficient for martingales of special form) conditions for the martingale closure from the right in the sense of theA-integral are given. These results follow from the theorem about passing to the limit under theA-integral. The theorem is established using the criterion for transposing iterated limits with respect to the base. It is shown that the sufficient conditions thus obtained are stronger than those previously known. Translated fromMatematicheskie Zametki, Vol.68, No. 1, pp. 98–104, July, 2000.