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Base-Invariance Implies Benford's Law
Proceedings of the American Mathematical Society
  • Theodore P. Hill, Georgia Institute of Technology - Main Campus
Publication Date

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 σ-algebra on the positive reals, and results for invariant measures on the circle.

Citation Information
Theodore P. Hill. "Base-Invariance Implies Benford's Law" Proceedings of the American Mathematical Society Vol. 123 Iss. 3 (1995) p. 887 - 895
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