We give an extension of Benford's law (first digit problem) by using the concept of conditional density, introduced by Fuchs and Letta. The main tool is the notion of regular subset of integers.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-3, author = {Rita Giuliano Antonini and Georges Grekos}, title = {Regular sets and conditional density: an extension of Benford's law}, journal = {Colloquium Mathematicae}, volume = {103}, year = {2005}, pages = {173-192}, zbl = {1092.11009}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-3} }
Rita Giuliano Antonini; Georges Grekos. Regular sets and conditional density: an extension of Benford's law. Colloquium Mathematicae, Tome 103 (2005) pp. 173-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-3/