On strong uniform distribution, II. The infinite-dimensional case
Volume 84 / 1998
Acta Arithmetica 84 (1998), 279-290
DOI: 10.4064/aa-84-3-279-290
Abstract
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.
