Geodesic
A note concerning the L1convergence of a class of games which become fairer with time
Glasgow mathematical journal, Tome 13 (1972) no. 1, pp. 39-41

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Throughout this note, let be a probability space with an increasing sequence of sub σ-fields of whose union generates . Let be a sequence of random variables adapted to (see [3], p. 65) and henceforth be referred to as a game. As in [1], the game will be said to become fairer with time if, for every ε > ε,as n, m → ∞ with n ≧ m 
Blake, Louis H. A note concerning the L1convergence of a class of games which become fairer with time. Glasgow mathematical journal, Tome 13 (1972) no. 1, pp. 39-41. doi: 10.1017/S0017089500001348
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[1] 1.Blake, L. H., A generalization of martingales and two consequent convergence theorems, Pacific J. Math., 35 (1970), 279–283. Google Scholar | DOI

[2] 2.Dunford, N. and Schwartz, J. T., Linear operators, Part I (New York, 1958). Google Scholar

[3] 3.Meyer, P. A., Probability and potentials (Waltham, Mass., 1966). Google Scholar

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