On Benford's law (Q760724)

The author considers the set of all positive integers as a model population, which contains the set of significant figures of all possible physical constants, past, present and future. For polynomial sampling procedures, he proves that randomly sampled integers from the population do not necessarily obey \textit{F. Benford}'s law [Proc. Am. Philos. Soc. 78, 551--572 (1938; Zbl 0018.26502)] but their Banach limit does. Benford's law is also proved for geometrical sampling procedures and for linear recurrence sampling procedures.