In this paper memoryless channels with general alphabets and input constraint are considered. Sufficient conditions are given that channel capacity can be approached by discrete input distributions or by uniform input distributions with finite support. As an example, the additive white Gaussian noise channel is considered.

The relationship between weak convergence of channel probability measures, channel capacity, and error probability of block codes is examined for memoryless channels with general input and output alphabets. It is shown that channel capacity is a lower semi-continuous function and that every block code with maximal probability of error /spl delta/ for a nominal channel for any /spl epsiv/>0 can be modified such that the modification has a probability of error less than /spl delta/+/spl epsiv/ for all channels in a sufficiently small neighborhood of the nominal channel.