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Sur le problème du premier chiffre décimal. (French) Zbl 0557.60011
Given $$E_k$$, the set of positive integers whose first digit is $$k$$, its asymptotic density does not exist (as it is well-known). In this paper it is proved that the analytical density $$d(E_ k)$$ exists, with $$d(E_k)=\log_{10}(1+1/k)$$, in accordance with known empirical results (the so-called ”first-digit problem”).
Reviewer: R.Scozzafava

##### MSC:
 60B99 Probability theory on algebraic and topological structures 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
##### Keywords:
asymptotic density; analytical density; first-digit problem