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.
Bibtex:
@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 = {http://dx.doi.org/10.2307/2160815},
}
Reference Type: Journal Article
Subject Area(s): Analysis, Measure Theory