Base-invariance implies Benford’s law
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- by Theodore P. Hill
- Proc. Amer. Math. Soc. 123 (1995), 887-895
- DOI: https://doi.org/10.1090/S0002-9939-1995-1233974-8
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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 $\sigma$-algebra on the positive reals, and results for invariant measures on the circle.References
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Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 887-895
- MSC: Primary 60A10; Secondary 28D05
- DOI: https://doi.org/10.1090/S0002-9939-1995-1233974-8
- MathSciNet review: 1233974