Geodesic
On strong uniform distribution, II. The infinite-dimensional case
Acta Arithmetica, Tome 84 (1998) no. 3, pp. 279-290.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/aa-84-3-279-290
Keywords: dimension, chains, almost sure convergence, universally good, density

Y. Lacroix 1

1 
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Y. Lacroix. On strong uniform distribution, II. The infinite-dimensional case. Acta Arithmetica, Tome 84 (1998) no. 3, pp. 279-290. doi : 10.4064/aa-84-3-279-290. http://geodesic.mathdoc.fr/articles/10.4064/aa-84-3-279-290/

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