  In 1910 Einstein published a crucial aspect of his understanding of Boltzmann
entropy. He essentially argued that the likelihood function of any system
composed by two probabilistically independent subsystems {\it ought} to be
factorizable into the likelihood functions of each of the subsystems.
Consistently he was satisfied by the fact that Boltzmann (additive) entropy
fulfills this epistemologically fundamental requirement. We show here that
entropies (e.g., the $q$-entropy on which nonextensive statistical mechanics is
based) which generalize the BG one through violation of its well known
additivity can {\it also} fulfill the same requirement. This fact sheds light
on the very foundations of the connection between the micro- and macro-scopic
worlds.
