On weak convergence of probability measures, channel capacity andcode error probabilities

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 δ for a nominal channel for any ϵ>0 can be modified such that the modification has a probability of error less than δ+ϵ for all channels in a sufficiently small neighborhood of the nominal channel