Abstract
We construct infinite dimensional chains that are L 1 good for almost sure convergence, which settles a question raised in this journal (7) and earlier in (6) by R. Nair. In (7) it was stated that the construction proposed in (4) was invalid. We complete the construction proposed in (4), where it is true that a piece of proof was forgotten. The technic remains the same and the completion of the proof rather natural.
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