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Uniformly maldistributed sequences in a strict sense

Authors:

Oto Strauch

Institution:

1. Mathematical Institute, Slovak Academy of Sciences, ?tefánikova 49, 814 73, Bratislava, Slovakia

Abstract:

It is shown that the following three limits

$\begin{gathered} \mathop {\lim }\limits_{n \to \infty } \frac{1}{{N^2 }}\sum\limits_{m,n = 1}^N {\|x_m - x_n \| = 0,} \hfill \\ \mathop {\lim \inf }\limits_{N \to \infty } \frac{1}{N}\sum\limits_{n = 1}^N {x_n = 0,\mathop {\lim \sup }\limits_{N \to \infty } } \frac{1}{N}\sum\limits_{n = 1}^N {x_n = 1} \hfill \\ \end{gathered}$

Keywords:	AMS subject Classification (1991)" target="_blank">AMS subject Classification (1991) Primary 11K06 11K31
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