We clarify questions related to the convergence of the OPE and conformal
block decomposition in unitary Conformal Field Theories (for any number of
spacetime dimensions). In particular, we explain why these expansions are
convergent in a finite region. We also show that the convergence is
exponentially fast, in the sense that the operators of dimension above Delta
contribute to correlation functions at most exp(-a Delta). Here the constant
a>0 depends on the positions of operator insertions and we compute it
explicitly.Comment: 26 pages, 6 figures; v2: a clarifying note and two refs added; v3:
note added concerning an extra constant factor in the main error estimate,
misprint correcte
