  Evaluating the channel capacity is one of many key problems in information
theory. In this work we derive rather-mild sufficient conditions under which
the capacity is finite and achievable. These conditions are derived for
generic, memoryless and possibly non-linear additive noise channels. The
results are based on a novel sufficient condition that guarantees the
convergence of differential entropies under point-wise convergence of
Probability Density Functions. Perhaps surprisingly, the finiteness of channel
capacity holds for the majority of setups, including those where inputs and
outputs have possibly infinite second-moments.
