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A note concerning the L1convergence of a class of games which become fairer with time

Published online by Cambridge University Press:  18 May 2009

Louis H. Blake
Louis H. Blake
Affiliation:
Worcester Polytechnic Institute, Worcester, Massachusetts 01609
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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

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 1 , March 1972 , pp. 39 - 41
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

1.Blake, L. H., A generalization of martingales and two consequent convergence theorems, Pacific J. Math., 35 (1970), 279–283.CrossRefGoogle Scholar
2.Dunford, N. and Schwartz, J. T., Linear operators, Part I (New York, 1958).Google Scholar
3.Meyer, P. A., Probability and potentials (Waltham, Mass., 1966).Google Scholar