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On uniform distribution of double sequences

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Abstract

In this paper a new notion of uniform distribution of double sequences is introduced. In the most elementary case a double sequence (xmn)m, n∈N is called uniformly distributed in this sense if all finite matrices of equal size appear with the same frequency as submatrices of the infinite matrix (xmn). Some special double sequences with such a distribution property are studied and metric theorems are proved.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, der Technischen Universität Wien, Gußhausstr. 27-29, 1040, Wien, Austria

    Peter Kirschenhofer

  2. Institut für Mathemat. Analysis, der Technischen Universität Wien, Gußhausstr. 27-29, 1040, Wien, Austria

    Robert F. Tichy

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  1. Peter Kirschenhofer
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  2. Robert F. Tichy
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Kirschenhofer, P., Tichy, R.F. On uniform distribution of double sequences. Manuscripta Math 35, 195–207 (1981). https://doi.org/10.1007/BF01168456

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  • DOI: https://doi.org/10.1007/BF01168456

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