Tsallis' Statistics without probability distributions. REPLY to Comment on "Possible Divergences in Tsallis' Thermostatistics"

In a recent letter (EPL, 104 (2013) 60003) we suggested a way to avoid divergences inherent to the formulation of nonextensive statistical mechanics. They can be eliminated via the use of a q-Laplace transformation, which was illustrated for the case of the harmonic oscillator. Lutsko and Boon now contend, in an interesting comment, that our new formulation raises questions that they carefully discuss. Here we elaborate an explanation of the contents of (EPL, 104 (2013) 60003) that permits to appreciate our original Letter in a more positive fashion.