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Jech, T (1992)

The Logarithmic Distribution of Leading Digits and Finitely Additive Measures

Discrete Mathematics 108(1-3), pp. 53-57.

ISSN/ISBN: 0012-365X DOI: 10.1016/0012-365X(92)90659-4

Abstract: A number of papers have been written to deal with the "first digit phenomenon", giving explanations using various summation methods or de nitions of probability. On close inspection, all these methods attempt to introduce a ( finitely additive) probability measure for which the distribution of leading digits satis es the logarithmic law. In this note we state necessary and sucient conditions for a probability measure to satisfy the rst digit law, and discuss various results and proposed explanations in the light of these conditions.

@article {MR1189828, AUTHOR = {Jech, Thomas}, TITLE = {The logarithmic distribution of leading digits and finitely additive measures}, NOTE = {Topological, algebraical and combinatorial structures. Frol{\'{\i}}k's memorial volume}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {108}, YEAR = {1992}, NUMBER = {1-3}, PAGES = {53--57}, ISSN = {0012-365X}, CODEN = {DSMHA4}, MRCLASS = {11K16 (11K55)}, MRNUMBER = {1189828 (93i:11087)}, MRREVIEWER = {Kazuo Goto}, DOI = {10.1016/0012-365X(92)90659-4}, URL = {}, }

Reference Type: Journal Article

Subject Area(s): Measure Theory