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Shorter Notes: A Short Proof of the Martingale Convergence Theorem

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 L1-bounded martingale theorem to the uniformly integrable case. A simple method... Full description

1st Person: Lamb, Charles W.
Source: in Proceedings of the American Mathematical Society Vol. 38, No. 1 (1973), p. 215-217
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Type of Publication: Article
Language: English
Published: 1973
Keywords: research-article
Online: Volltext
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