Base-Invariance Implies Benford's LawProceedings of the American Mathematical Society
AbstractA 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 InformationTheodore P. Hill. "Base-Invariance Implies Benford's Law" Proceedings of the American Mathematical Society Vol. 123 Iss. 3 (1995) p. 887 - 895
Available at: http://works.bepress.com/tphill/49/