an:00741416
Zbl 0813.60002
Hill, Theodore P.
Base-invariance implies Benford's law
EN
Proc. Am. Math. Soc. 123, No. 3, 887-895 (1995).
0002-9939 1088-6826
1995
j
60A10 28D05
Benford's law or the first-digit phenomenon; base-invariant distributions; extremal probabilities; results for invariant measures
Summary: 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.