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Jun 3, 2018 at 23:43 comment added 0xbadf00d Since a martingale is required to be adapted, we'll need completeness of the filtration for the conclusion from the $L^1$-convergence.
Jan 22, 2016 at 18:24 vote accept Ben
Jan 22, 2016 at 15:47 history answered Nate Eldredge CC BY-SA 3.0