Geodesic
A Ratio Limit Theorem for Approximate Martingales
Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 772-779

Voir la notice de l'article provenant de la source Cambridge University Press

It has been proved [3, p. 630] that the martingale convergence theorem obtained by Andersen and Jessen [1, p. 5] follows from the classical theory developed by Doob. By using some results of Yosida and Hewitt [9] on finitely additive set functions, Johansen and Karush [7] proved that the identification of the limit function as a derivative in the approach of Andersen and Jessen can be obtained in the general case. In this paper we sharpen the methods of Andersen and Jessen to obtain a ratio limit theorem for “approximate martingales”. 
Lamb, Charles W. A Ratio Limit Theorem for Approximate Martingales. Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 772-779. doi: 10.4153/CJM-1973-079-6
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