Baseinvariance implies Benford’s law
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 by Theodore P. Hill PDF
 Proc. Amer. Math. Soc. 123 (1995), 887895 Request permission
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 $\sigma$algebra on the positive reals, and results for invariant measures on the circle.References

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Additional Information
 © Copyright 1995 American Mathematical Society
 Journal: Proc. Amer. Math. Soc. 123 (1995), 887895
 MSC: Primary 60A10; Secondary 28D05
 DOI: https://doi.org/10.1090/S00029939199512339748
 MathSciNet review: 1233974