On Uniform Distribution Modulo 1 and Functional Convergence

Paštéka, Milan

doi:10.2478/udt-2024-0004

Abstract

In this note, we study the convergence of functional sequences. A criterion for uniform distribution mod 1 is derived. Then we study the partitions, block sequences and the uniform distribution preserving mappings. In the last part, we prove that to each one to one sequence dense in [0, 1] a regular matrix summation method such that this sequence is uniformly distributed mod 1 with respect to this method exists.

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On Uniform Distribution Modulo 1 and Functional Convergence

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