For a weakly continuous stationary channel with operational sliding-block capacity

, it is shown that every stationary, ergodic, aperiodic source with entropy less than

is sliding-block transmissible over the channel. It had been shown earlier that a stationary and ergodic source is block transmissible over the channel if its entropy is less than the operational block capacity

. If, in addition, the channel is ergodic, it is shown that

. An example of a nonergodic weakly continuous channel is given for which

.