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ArticleOriginal scientific text

Title

On strong uniform distribution, II. The infinite-dimensional case

Authors 1

Affiliations

  1. Département de Mathématiques, Faculté des Sciences, Université de Bretagne Occidentale, 6 Avenue V. Le Gorgeu, B.P. 809, 29285 Brest Cedex, France

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.

Keywords

ENG
dimension, chains, almost sure convergence, universally good, density

Bibliography

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Acta Arithmetica
1998/84/3
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Pages:
279-290
Main language of publication
English
Received
1997-06-17
Accepted
1997-11-25
Published
1998
Exact and natural sciences