Lolbert, Tamás On the non-existence of a general Benford’s law. (English) Zbl 1140.60003 Math. Soc. Sci. 55, No. 2, 103-106 (2008). Benford’s law states that in arbitrary collected ensemble of (real world) data certain digits appear more often as leading digits than others. More formally the mantissae follow a logarithmic distribution accordingly to the base representation that is chosen. In these short communication the author shows by a simple contradiction that if there was probability measure such that fulfills Benford’s law simultaniously for an unbounded number of bases this leads to a contradiction. Reviewer: Michael Högele (Berlin) Cited in 1 Document MSC: 60A10 Probabilistic measure theory 60E10 Characteristic functions; other transforms 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. Keywords:Benford’s law; leading digit distribution; mantissae; logarithmic distribution × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Benford, F., The law of anomalous numbers, Proceedings of the American Philosophical Society, 78, 551-572 (1938) · Zbl 0018.26502 [2] Hill, T. P., Base-invariance implies Benford’s law, Proceedings of the American Mathematical Society, 123, 887-895 (1995) · Zbl 0813.60002 [3] Hill, T. P., A statistical derivation of the significant-digit law, Statistical Science, 10, 354-363 (1996) · Zbl 0955.60509 [4] Newcomb, S., Note on the frequency of use of the different digits in natural numbers, American Journal of Mathematics, 4, 39-40 (1881) · JFM 13.0161.01 [5] Raimi, R. A., The first digit problem, American Mathematical Monthly, 83, 521-538 (1976) · Zbl 0349.60014 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.