Baseinvariance implies Benford's law
Author:
Theodore P. Hill
Journal:
Proc. Amer. Math. Soc. 123 (1995), 887895
MSC:
Primary 60A10; Secondary 28D05
MathSciNet review:
1233974
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Abstract: A derivation of Benford's Law or the FirstDigit Phenomenon is given assuming only baseinvariance of the underlying law. The only baseinvariant distributions are shown to be convex combinations of two extremal probabilities, one corresponding to point mass and the other a logLebesgue measure. The main tools in the proof are identification of an appropriate mantissa algebra on the positive reals, and results for invariant measures on the circle.
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 S. Newcomb, Note on the frequency of use of the different digits in natural numbers, Amer. J. Math. 4 (1881), 3940. MR 1505286
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199512339748
PII:
S 00029939(1995)12339748
Keywords:
Firstdigit problem,
baseinvariance,
scaleinvariance,
Benford's Law,
invariant measure,
nth digit law
Article copyright:
© Copyright 1995
American Mathematical Society
