On strong uniform distribution, II. The infinite-dimensional case
Y. Lacroix
Acta Arithmetica, Tome 84 (1998), p. 279-290 / Harvested from The Polish Digital Mathematics Library
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We construct infinite-dimensional chains that are L¹ good for almost sure convergence, which settles a question raised in this journal [N]. We give some conditions for a coprime generated chain to be bad for L² or L∞, using the entropy method. It follows that such a chain with positive lower density is bad for L∞. There also exist such bad chains with zero density.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:207146 
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Y. Lacroix. On strong uniform distribution, II. The infinite-dimensional case. Acta Arithmetica, Tome 84 (1998) pp. 279-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav84i3p279bwm/

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