  For the class of mixed channels decomposed into stationary memoryless
channels, single-letter characterizations of the $\varepsilon$-capacity have
not been known except for restricted classes of channels such as the regular
decomposable channel introduced by Winkelbauer. This paper gives single-letter
characterizations of $\varepsilon$-capacity for mixed channels decomposed into
at most countably many memoryless channels with a finite input alphabet and a
general output alphabet with/without cost constraints. It is shown that a given
characterization reduces to the one for the channel capacity given by Ahlswede
when $\varepsilon$ is zero. In the proof of the coding theorem, the meta
converse bound, originally given by Polyanskiy, Poor and Verd\'u, is
particularized for the mixed channel decomposed into general component
channels.
