Mathematical Notes

, Volume 88, Issue 3, pp 449–463

Benford’s law and distribution functions of sequences in (0, 1)


DOI: 10.1134/S0001434610090178

Cite this article as:
Baláž, V., Nagasaka, K. & Strauch, O. Math Notes (2010) 88: 449. doi:10.1134/S0001434610090178


Applying the theory of distribution functions of sequences xn ∈ [0, 1], n = 1, 2, ..., we find a functional equation for distribution functions of a sequence xn and show that the satisfaction of this functional equation for a sequence xn is equivalent to the fact that the sequence xn to satisfies the strong Benford law. Examples of distribution functions of sequences satisfying the functional equation are given with an application to the strong Benford law in different bases. Several direct consequences from uniform distribution theory are shown for the strong Benford law.

Key words

distribution function of a sequence Benford’s law density of occurrence of digits 

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Slovak Technical UniversityBratislavaSlovakia
  2. 2.Hosei UniversityTokyoJapan
  3. 3.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovakia

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