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A short proof of the martingale convergence theorem

Author: Charles W. Lamb
Journal: Proc. Amer. Math. Soc. 38 (1973), 215-217
MSC: Primary 60G45
MathSciNet review: 0324770
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Abstract: The martingale convergence theorem is first proved for uniformly integrable martingales by a standard application of Doob's maximal inequality. A simple truncation argument is then given which reduces the proof of the $ {L^1}$-bounded martingale theorem to the uniformly integrable case. A similar method is used to prove Burkholder's martingale transform convergence theorem.

References [Enhancements On Off] (What's this?)

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  • [3] Adriano M. Garsia, Topics in almost everywhere convergence, Lectures in Advanced Mathematics, vol. 4, Markham Publishing Co., Chicago, Ill., 1970. MR 0261253
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Article copyright: © Copyright 1973 American Mathematical Society