On Benford's law to variable base

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Abstract

Benford's law is studied in dependence on the base b> 1. It can hold to large bases b only approximately. The quality of approximation is estimated in cases of products and sums of random variables, respectively, and in case of some deterministic sequences. Always the approximation by Benford's law becomes worse as b → ∞, but as a rule also as b → 1 + 0.

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