We propose a probabilistic interpretation of Benford’s law, which
predicts the probability distribution of all digits in everyday-life numbers. Heuri-
stically, our point of view consists in considering an everyday-life number as a
continuous random variable taking value in an interval [0,A], whose maximum
A is itself an everyday-life number. This approach can be linked to the chara-
cterization of Benford’s law by scale-invariance, as well as to the convergence
of a product of independent random variables to Benford’s law. It also allows
to generalize Flehinger’s result about the convergence of iterations of Cesaro-
averages to Benford’s la
