Abstract
In their paperSome finitely additive probability (to appear in Ann. Probability), Roger A. Purves and William D. Sudderth introduced the measurable strategy idea. In this paper, we first generalize the measurable strategy idea to the more general sigma-fields of subsets ofX and prove an important theorem. Then, based on this theorem, we state and prove a finitely additive version of Kolmogorov’s law of the iterated logarithm and a finitely additive version of Hartman and Wintner’s law of the iterated logarithm in a finitely additive setting.
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This research was written with the partial support of the U.S. Army Grant DA-ARO-D-31-124-70-G-102.
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Chen, R. A finitely additive version of kolmogorov’s law of the iterated logarithm. Israel J. Math. 23, 209–220 (1976). https://doi.org/10.1007/BF02761801
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DOI: https://doi.org/10.1007/BF02761801