Base-invariance implies Benford's law

Author:
Theodore P. Hill

Journal:
Proc. Amer. Math. Soc. **123** (1995), 887-895

MSC:
Primary 60A10; Secondary 28D05

MathSciNet review:
1233974

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Abstract: A derivation of Benford's Law or the First-Digit Phenomenon is given assuming only base-invariance of the underlying law. The only base-invariant distributions are shown to be convex combinations of two extremal probabilities, one corresponding to point mass and the other a log-Lebesgue 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1233974-8

Keywords:
First-digit problem,
base-invariance,
scale-invariance,
Benford's Law,
invariant measure,
*n*th digit law

Article copyright:
© Copyright 1995
American Mathematical Society