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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 19. Issue 1 & 2


Published on

December, 2024


Pages

33-42


DOI

https://doi.org/10.2478/udt-2024-0004

Article

On Uniform Distribution Modulo 1 and Functional Convergence


Authors

Milan Paštéka


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.


Citation

Paštéka, M. (2024). On Uniform Distribution Modulo 1 and Functional Convergence. Uniform distribution theory, 19(1-2), 33-42. https://doi.org/10.2478/udt-2024-0004