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Hill, TP (1995)

Base-Invariance Implies Benford's Law

Proceedings of the American Mathematical Society 123(3), pp. 887-895.

ISSN/ISBN: 0002-9939 DOI: 10.2307/2160815

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

@article {MR1233974, AUTHOR = {Hill, Theodore P.}, TITLE = {Base-invariance implies {B}enford's law}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {123}, YEAR = {1995}, NUMBER = {3}, PAGES = {887--895}, ISSN = {0002-9939}, CODEN = {PAMYAR}, MRCLASS = {60A10 (28D05)}, MRNUMBER = {1233974 (95d:60006)}, MRREVIEWER = {Peter Schatte}, DOI = {10.2307/2160815}, URL = {}, }

Reference Type: Journal Article

Subject Area(s): Analysis, Measure Theory