Title: On the putative essential discreteness of q-generalized entropies,
Abstract: It has been argued in [EPL {\bf 90} (2010) 50004], entitled {\it Essential
discreteness in generalized thermostatistics with non-logarithmic entropy},
that "continuous Hamiltonian systems with long-range interactions and the
so-called q-Gaussian momentum distributions are seen to be outside the scope of
non-extensive statistical mechanics". The arguments are clever and appealing.
We show here that, however, some mathematical subtleties render them
unconvincing