On Strong Uniform Distribution, III

We construct infinite dimensional chains that are 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.